The Warburg impedance response [1] in electrochemical impedance spectroscopy data is commonly recognized as a signature of molecular diffusion processes. One can go beyond a qualitative perspective based on equivalent circuits and employ impedance data to quantify material properties relevant to transport phenomena. The Warburg impedance in particular provides useful data for electrolyte characterization. More often than not, however, properties such as transference numbers and diffusivities have been extracted by applying the Poisson-Nernst-Planck (PNP) model [2] to impedance data; the PNP model neglects Darken factors, and therefore does not bear accurate results when applied to concentrated solutions.

This work builds on the detailed impedance formulation discussed by Pollard and Comte [3], who rely on Onsager-Stefan-Maxwell theory instead of PNP theory. As well as accounting for thermodynamic factors and using thermodynamically meaningful potentials [4], the Pollard-Comte model involves parameters that quantify solute-volume effects, namely, the excluded-volume effect and Faradaic convection [5]. Faradaic convection, which refers to bulk electrolyte flow induced by interfacial electrochemical reactions, is one instance of the electrochemical/mechanical coupling this presentation will explore. The Pollard-Comte analysis is extended to an asymmetric cell, in which different half-reactions occur at the working and counter electrodes.

Faradaic convection is an essentially kinematic phenomenon. A far more substantial augmentation of the Pollard-Comte model is needed to account for dynamical effects, such as those arising from local pressure variations. Liu and Monroe showed that in multiple spatial dimensions, Newman’s concentrated-solution theory requires a local momentum balance in addition to the volume-explicit equation of state [5]. Appending the momentum balance, and its associated state-variable definitions and constitutive laws, is a non-trivial exercise, because the pressure dependence of partial molar volumes makes the governing system of transport equations highly coupled – even in a one-dimensional case.

Mechanical responses whose characteristic times differ substantially from those associated with molecular diffusion or capacitive relaxation arise from both liquid inertia and viscosity. Impedance analysis is therefore a good strategy for deconvoluting dynamical effects and validating the augmented transport model. It also appears that mechanical effects may be associated with new impedance elements that have not been considered to date.

 

 

References

1. E. Warburg, Annalen der Physik und Chemie 67, 493 (1899)

2. D.R. Franceschetti, J.R. Macdonald, and R.P. Buck, J Electrochem Soc, 138, 1368 (1991)

3. R. Pollard and T. Comte, J Electrochem Soc, 136, 3734 (1989)

4. A.M. Bizeray, D.A. Howey, and C.W. Monroe, J Electrochem Soc, 163, E223 (2016)

5. J. Liu and C.W. Monroe, Electrochim Acta, 135, 447 (2014)