Numerical investigations of solution resistance effects on nonlinear electrochemical impedance spectra

Abstract

The effect of solution resistance on the nonlinear electrochemical impedance spectra under quasi-potentiostatic conditions was investigated by numerical simulations. An electron transfer reaction, a reaction with an adsorbed intermediate and a reaction exhibiting negative resistance were chosen as the candidates and large amplitude perturbations were employed. The potential across the interface drifts initially and stabilizes after a certain time, which depends on the solution resistance and the kinetic parameter values. The fraction of the applied potential drop occurring across the metal-solution interface depends on the frequency and the amplitude of the perturbation as well as the value of solution resistance. This in turn leads to the possibility that, for a given conditions, a part of the spectrum may be acquired in the linear regime while the remaining part may be acquired in the nonlinear regime. The sensitivity of the Kramers Kronig transform (KKT) to identify these cases is evaluated. The results show that although the spectra are distorted by poorly conducting solution, the sensitivity of KKT to identify the nonlinear effects is not enhanced by the introduction of significant solution resistance.

Review—Nonlinear Electrochemical Impedance Spectroscopy

“…When mass transfer is rapid but R sol is not negligible, the governing equations can be solved numerically to calculate the impedance spectra at any frequency. [43][44][45][46] Kramers Kronig Transforms (KKT) are mathematical equations that can be used to confirm that the response arise from a system which is linear, causal and stable. While KKT are successful in flagging violations of stability, 47 they are only partially successful in identifying nonlinearity effects.…”

“…21 If the impedance is acquired under pseudo potentiostatic conditions, when R sol is significant and perturbation amplitude is large, the potential drop across electrode-electroyte interface will not be sinusoidal even if the potential applied across the entire system is sinusoidal. [13][14][15]46 Initially, it was though that R p,NL in these cases will always decrease with E ac0 , but it was later shown that R p,NL may increase or decrease with E ac0 depending on the value of bias potential (E dc ) and R sol . [13][14][15] Expressions were also derived for R p,NL for electrochemical reactions obeying Tafel, or Butler Volmer or Nernst law or an electron transfer reaction coupled with electrochemical adsorption reaction (E-EAR), when NLEIS was measured under potentiostatic or galvanostatic conditions.. [13][14][15] In corrosion studies, it is desirable to measure the linear polarization resistance (R p ) quickly and independently of polarization experiments.…”

“…Hence EIS data must be recorded after allowing sufficient time for the surface coverage values to settle. The drift effect is more pronounced when the R sol is high 46 and this was illustrated for reaction with two adsorbed intermediates, exhibiting a variety of patterns in complex plane plots. Using a heuristic approach, an estimate for R t,NL for the reaction in Eq.…”

“…Using the proposed numerical simulation method, the nonlinear impedance of other complicated reactions can also be predicted. 27,46,47 In addition to calculating the values at fundamental frequency, the higher harmonics can easily be computed. NLEIS data were simulated numerically to understand the capability of KKT to detect nonlinearities in the data.…”

Multi-Sine EIS- Drift, Non Linearity and Solution Resistance Effects

“…9 must be used along with the other equations to simulate the impedance spectra. In these cases, upon applying the ac potential, the systems takes some time to yield steady periodic current (18). The simulations were performed such that sufficient wait time was given to achieve steady periodic current at each frequency and the data collected subsequently was analyzed.…”