Development of a Physics-Based Analytical Impedance Model in Vanadium Redox Flow Batteries: Insight into Local Mass Transport Losses
Authors: Messaggi Mirko , Casalegno Andrea , Zago Matteo 
Published: July 2022

Vanadium redox flow battery (VRFB) is a promising technology for energy storage because of its independent energy to power ratio and long cycle life. However, VRFB commercialization is still hindered by some technological issues, among which the mass transport of the electrolyte over the porous electrode is one of the most important, since it leads to increased overpotential at high current and limits the power density of the system. Electrolyte mass transport is regulated by different physical phenomena, occurring at different scale (channel, electrode, pore) with different intensity throughout cell active area. Therefore, the quantification of the corresponding performance loss is crucial in order to improve VRFB competitiveness.
Electrochemical impedance spectroscopy (EIS) is a powerful in-situ measurement technique that permits to separate physical phenomena characterized by different relaxation frequencies. However, despite its potentialities, the interpretation of experiments is not trivial and physics-based modelling plays a key role to derive quantitative information [1].
In this work, local impedance spectra were measured in 10 different regions of a 25 cm2 segmented cell [2] at different electrolyte flow rates and current densities, adopting symmetric cell configuration with both positive and negative electrolyte. Impedance spectra were recorded in a frequency range included between 10 kHz to 10 mHz. The cell hardware was composed by single serpentine graphite distributors, manufactured in-house with the 10 electrically insulated regions held together by means of a 0.8 mm layer of insulating inert epoxy resin. Both positive and negative electrodes were Sigracet® 39 AA.
The local impedance spectra were subsequently analyzed with the aid of a 1D+1D physics-based analytical model, able to compute system EIS with a reduced computational time. The developed model coupled the electrochemistry of red-ox reactions with different electrolyte mass transport mechanisms, each associated to an impedance (i.e., voltage loss). Electrolyte is firstly transported along the channel, which is responsible for an impedance related to vanadium consumption and where a convective mass transport resistance at the channel/electrode interface accounts the voltage loss due to the concentration gradients between the channel and the electrode. Then vanadium ions are transported through the porous electrode and from the bulk of electrode pores to the active surface of the carbon fibers, where red-ox reactions occur.
The model was validated with respect to local impedance spectra: Figure 1 illustrates an example in the case of symmetric cell with negative electrolyte at 0.1 A cm2 and 20 ml min-1. It can be noticed that the developed model reproduces with an acceptable accuracy the local EIS, permitting to quantify the contribution of different mass transport losses throughout cell active area. In order to correctly reproduce the evolution of impedance along channel length it was fundamental to consider the propagation of the state of charge oscillation along the channel, which is induced by the local oscillating consumption of reactants. This induces the reactions occurring in the downstream portion of the electrode to experience an oscillating reactants concentration.

Figure 1 – Comparison between simulated and measured impedance spectra along channel length in symmetric cell with negative electrolyte at 0.1 A cm-2 and 20 ml min-1.

For the negative electrode, in most of the investigated conditions the voltage loss associated to the electrolyte transport from the bulk of the pores to the surface of carbon fibres appears predominant compared to the other transport mechanisms, while the greatest contribution is given by kinetic losses. Moreover, all the contributions are substantially uniform along the channel length, except for the increasing effect of state of charge oscillation propagation.
For the positive electrode, the greatest contribution turns out to be the transport through the electrode thickness at high flow rate, while at low flow rate the most relevant effect is related to mass transport at channel-electrode interface. Along the channel length, all the mass transport contributions show a slight increase, but the greatest variation is observed once again for the state of charge oscillation propagation.

References:

[1] M. Zago et al., Electrochimica Acta 248 (2017) 505-517.
[2] M. Messaggi et al., Journal of Power Sources 449 (2020) 227588.

Figure 1