PRECISION OF IMPEDANCE SPECTROSCOPY ESTIMATES OF BULK, REACTION-RATE, AND DIFFUSION PARAMETERS

Complex least squares fitting and Monte Carlo simulation have been used to generate numerical values for the ultimate precision with which various impedance spectroscopy fitting-model parameters can be estimated by complex nonlinear least squares fitting. Results are presented in terms of normalized relative standard deviations for bulk, reaction-rate, and diffusion parameters. The analysis applies only in the usual case where errors in the data are proportional to the data values themselves (constant percentage error). By using special normalization, we ensure that our results are of universal applicability and may be used for prediction and comparison of data situations with an arbitrary number of data values and for any reasonable effort percentage. The results may be used in the design of experiments to predict, before any measurements are carried out, how accurately various fitting parameters can be determined for an assumed amount of error and a particular number of data points. Alternatively, they may be employed to evaluate the minimum expected uncertainty bounds of parameter estimates already obtained from complex nonlinear least squares fitting for comparison with the actual bounds obtained from the fitting. The results apply to several finite-length-diffusion situations, including restricted and ordinary diffusion of charged species and diffusion of neutral entities. We find that, depending on the specific fitting model and parameter values, there are some limiting situations where bulk resistance, reaction resistance, or diffusion exchange rate cannot be estimated with adequate precision by complex nonlinear least squares fitting.