On the Error Structure of Impedance Measurements Series Expansions

A framework is presented for characterizing the statistical properties of frequency-domain measurements. The correlation between the variance in the complex impedance and the variances in the complex current and voltage are examined by means of a Taylor series expansion for the impedance. Both sufficient-only and necessary and sufficient conditions for equality of the variances of real and imaginary impedance are identified and verified using stochastic simulations of techniques commonly employed in frequency-domain measurements.

[1]  U. Bertocci,et al.  Noise Resistance Applied to Corrosion Measurements III. Influence of the Instrumental Noise on the Measurements , 1997 .

[2]  Oliver C. Moghissi,et al.  Application of Measurement Models for Analysis of Impedance Spectra , 1993 .

[3]  J. J. García-Jareño,et al.  Charge compensation process in polypyrrole studied by ac electrogravimetry , 2001 .

[4]  Mark E. Orazem,et al.  Measurement Models for Electrochemical Impedance Spectroscopy I . Demonstration of Applicability , 1992 .

[5]  B. Tribollet,et al.  Thermoelectrochemical Transfer Function under Thermal Laminar Free Convection at a Vertical Electrode , 2000 .

[6]  On the transformation of colored random noise by the Kronig-Kramers integral transforms , 1997 .

[7]  J. Macdonald.  Some new directions in impedance spectroscopy data analysis , 1993 .

[8]  L. García-Rubio,et al.  Spectroscopy Applications of the Kramers‐Kronig Transforms: Implications for Error Structure Identification , 1997 .

[9]  F. Huet,et al.  Investigation of electrochemical processes by an electrochemical noise analysis. Theoretical and experimental aspects in potentiostatic regime , 1986 .

[10]  L. García-Rubio,et al.  Application of Measurement Models to Impedance Spectroscopy II . Determination of the Stochastic Contribution to the Error Structure , 1995 .

[11]  H. Takenouti,et al.  Copper dissolution in acidic sulphate media studied by QCM and rrde under ac signal , 1992 .

[12]  B. Tribollet,et al.  Relationship between the electrochemical impedance and the electrohydrodynamical impedances measured using a rotating disc electrode , 1980 .

[13]  J. Ross Macdonald,et al.  A flexible procedure for analyzing impedance spectroscopy results: Description and illustrations , 1987 .

[14]  D. Macdonald,et al.  Characterizing electrochemical systems in the frequency domain , 1998 .

[15]  G. W. Snedecor.  Statistical Methods , 1964 .

[16]  B. Tribollet,et al.  Flow Modulation Techniques in Electrochemistry , 1991 .

[17]  H. Takenouti,et al.  A new experimental approach to the time-constants of electrochemical impedance: frequency response of the double layer capacitance , 2001 .

[18]  J. S. Hunter,et al.  Statistics for experimenters : an introduction to design, data analysis, and model building , 1979 .

[19]  Siegmund Brandt,et al.  Statistical and Computational Methods in Data Analysis , 1971 .

[20]  B. Tribollet,et al.  A Transfer Function Approach for a Generalized Electrochemical Impedance Spectroscopy , 1994 .

[21]  W. Kenan,et al.  Impedance Spectroscopy: Emphasizing Solid Materials and Systems , 1987 .

[22]  P. Żółtowski.  The error function for fitting of models to immittance data , 1984 .

[23]  M. Orazem,et al.  The Error Structure of Impedance Spectra for Systems with a Large Ohmic Resistance with Respect to the Polarization Impedance , 1996 .

[24]  Mark E. Orazem,et al.  Development of physico-chemical models for electrochemical impedance spectroscopy , 1993 .

[25]  Oscar D. Crisalle,et al.  On the Error Structure of Impedance Measurements Simulation of FRA Instrumentation , 2003 .

[26]  D. Fermín,et al.  A kinetic study of CdS photocorrosion by intensity modulated photocurrent and photoelectrochemical impedance spectroscopy , 1999 .

[27]  James Ross Macdonald,et al.  IMPEDANCE SPECTROSCOPY: OLD PROBLEMS AND NEW DEVELOPMENTS , 1990 .

[28]  Mark E. Orazem,et al.  Application of Measurement Models to Impedance Spectroscopy III . Evaluation of Consistency with the Kramers‐Kronig Relations , 1995 .

[29]  J. Dygas,et al.  Variance of errors and elimination of outliers in the least squares analysis of impedance spectra , 1999 .

[30]  H. Takenouti,et al.  ac Response of a rotating ring—disk electrode: application to 2-D and 3-D film formation in anodic processes , 1989 .

[31]  Brian E. Conway,et al.  Modern Aspects of Electrochemistry , 1974 .