State of Charge and State of Health Assessment of Viologens in Aqueous‐Organic Redox‐Flow Electrolytes Using In Situ IR Spectroscopy and Multivariate Curve Resolution

Abstract Aqueous‐organic redox flow batteries (RFBs) have gained considerable interest in recent years, given their potential for an economically viable energy storage at large scale. This, however, strongly depends on both the robustness of the underlying electrolyte chemistry against molecular decomposition reactions as well as the device's operation. With regard to this, the presented study focuses on the use of in situ IR spectroscopy in combination with a multivariate curve resolution approach to gain insight into both the molecular structures of the active materials present within the electrolyte as well as crucial electrolyte state parameters, represented by the electrolyte's state of charge (SOC) and state of health (SOH). To demonstrate the general applicability of the approach, methyl viologen (MV) and bis(3‐trimethylammonium)propyl viologen (BTMAPV) are chosen, as viologens are frequently used as negolytes in aqueous‐organic RFBs. The study's findings highlight the impact of in situ spectroscopy and spectral deconvolution tools on the precision of the obtainable SOC and SOH values. Furthermore, the study indicates the occurrence of multiple viologen dimers, which possibly influence the electrolyte lifetime and charging characteristics.


Synthesis of 1,1'-bis(3-(trimethylammonio)propyl)-4,4'-bipyridinium tetra chloride
4,4'-Bipyridine (30 g, 192 mmol) and 3-chloro-N,N,N-trimethylpropan-1-ammonium bromide (91.5 g, 423 mmol) were suspended in dimethylformamide (250 mL) and heated to 125 °C. Upon heating the solids completely dissolved and a yellow/brownish solution was formed. After stirring at 125 °C for 18 h the brownish participate was filtered off, washed with acetone (3  100 mL) and subsequently with dichloromethane (3  100 mL) before it was dried under reduced pressure. The solid was heated under reflux in ethanol (300 mL) and subsequently filtrated as a hot solution. The product was purified via an ion exchange with Dowex Marathon A2 (50 g) in deionized water (300 mL). Subsequently, the solvent was removed under reduced pressure. The desired product was received as white powder (36.1 g, 37.5%) after drying for 48 h under reduced pressure (approximately 2 to 10 mbar) at 40 °C in a Binder vacuum drying oven. 1

Instruments
In situ infrared (IR) spectra were recorded using a liquid nitrogen-cooled ReactIR 701L (Mettler Toledo, Germany), equipped with a Micro Flow Cell DS DiComp (Mettler Toledo, Germany) between 650 and 4000 cm -1 at a resolution of 4 cm -1 . A background spectrum of deionized water was collected with 128 single scans prior to each experiment. Each individual in situ IR spectrum consists of 138 single scans, which corresponds to a measurement time of 90 s per spectrum. The same number of scans was used for the concentration calibration measurements of methyl viologen (MV) and 1,1'bis(3-(trimethylammonium)propyl)-4,4'-bipyridinium tetra chloride (BTMAPV) and their respective radical cations (MVRC and BTMAPVRC).
For reference purposes, an ATR-IR spectra of a MV and BTMAPV crystals were recorded between 550 and 4000 cm -1 with a resolution of 4 cm -1 using a ZnSe crystal on an iD7-ATR-IR Nicolet iS5 (Thermo Scientific, Massachusetts). The IR spectrum consists of 8 individual measurements where each measurement is made up of 32 single scans.
The refractive indices of all solutions were measured using a digital ORF 85BM refractometer by KERN & SOHN GmbH (Balingen, Germany) inside a glove box.

Data Preprocessing
The IR spectra were preprocessed using R (4.0.3) 4 and the preprocessing scheme previously published. 5 The figures were made using the R packages ggplot2 6 , dplyr 7 and gridExtra 8 . Firstly, the IR spectra were corrected for the influence of water vapor following a modified procedure from Bruun et al.. 9 For the correction only the wavenumber region from 1350 and 1840 cm -1 was used and corrected, respectively.
Following the water vapor correction, the IR spectra were corrected for the varying penetration depth of the IR light during the Attenuated Total Reflection (ATR) measurement mode. IR light of lower wavenumbers penetrates deeper into the sample than light of higher wavenumbers. Thus, the absorbance at lower wavenumbers is overestimated in ATR-IR compared to transmission IR. The concentration-dependent refractive index of all compounds in aqueous solution can be seen in Table  S3 to Table S6 and Figure S20 to Figure S23.
Subsequently, the IR spectra were cropped to the region of interest between 650 and 1750 cm -1 . Afterwards, the IR spectra were baseline-corrected using a SNIP algorithm 10,11 (iterations = 18, order = 2).
By using the Lambert-Beer-law, the wavenumber-dependent penetration depth d and the absorbances from the concentration calibration measurements A, it is possible to calculate the extinction coefficients of MV, MVRC, BTMAPV and BTMAPVRC in aqueous solution according to (1) where ε is the extinction coefficient, A the concentration-dependent IR absorbance, c the concentration and d the penetration depth. The most important IR bands of all components as well as their extinction coefficients are summarized in Table S1 and Table S2, respectively.

Data Analysis
An initial analysis was based on the previously described approach using a series of calibration measurements and Lambert-Beers law to extract the concentration of each species at every point in time from a series of IR spectra. This analysis worked well for the SOC determination but failed for an accurate SOH determination. Thus, a new analysis was developed.
The new approach is based on a Multivariante Curve Resolution -Alternating Least Square (MCR-ALS) algorithm as implanted by R package ALS. 12 (2) Where D is m x n data matrix (e.g. m IR spectra with n wavenumber positions recorded during RFB charging/discharging), C is a m x k concentration matrix, S T a k x n spectra matrix containing the spectral fingerprint of k components and E is a m x n residual error matrix.
Firstly, 1000 IR spectra measured during galvanostatic charging and discharging of a symmetrical compositionally-unbalanced 13,14 MV/MVRC RFB with a total electrolyte concentration of 1.5 M were analyzed using MCR-ALS. Both the spectral as well as the concentration matrix were locked to nonnegative values while the total concentration for each time point was locked to 1.5 M. The concentration matrix was initialized using the concentration values of MV and MVRC as extracted by the previous analysis based on Lambert-Beers law. The resulting spectra matrix S T was subsequently used in a Non-Negative Least Square (NNLS) fit 15 to analyze a new set of in situ IR spectra. The result is a concentration matrix which contains the concentration of each species at each time point. Thus, the result of the combined use of MCR-ALS and NNLS algorithms is a set of IR spectra each representing a component in the RFB and the concentration of each component at every measurement time. The same procedure was applied for the in situ spectra recorded from a BTMAPV/BTMAPVRC RFB using 1.2 M as the total concentration during MCR-ALS analysis.
The MCR-ALS extracted spectra were compared to the reference spectra recorded during the calibration experiments using Pearson correlation coefficient.
When the spectrum of a MCR-ALS component matched the spectrum of MVRC it was assigned as charged species, while it was assigned as an uncharged species if it matched the spectrum of MV. A MCR-ALS spectrum matched MVRC when the corresponding correlation coefficient was higher compared to the correlation coefficient between the component and MV. With this approach each MCR-ALS component was assigned either as a charged or uncharged species, respectively.
The SOC was calculated by comparing the concentration of all charged species to the total concentration of all species. The SOH was calculated by comparing the total concentration of all species to the total electrolyte concentration at a given reference point.
The number of components k in the MCR-ALS analysis can be freely chosen. The MCR-ALS/NNLS approach was tested using k = 2, 3, 4, 5 and 6 (see Error! Reference source not found., Error! Reference source not found. as well as Figure S3 - Figure S9). The quality of all MCR-ALS/NNLS fits was compared to the standard analysis offered by Lambert-Beers law. The quality of the respective MCR-ALS/NNLS fits was accessed based on a comparison to the recorded electrochemical data (voltage and current) for the SOC values. For the SOH analysis the aim was to achieve a low variability of the data as long as the SOH remained unchanged and to accurately represent the artificial drops in SOH induced throughout the experiment.

Open Circuit Voltage Experiments
The supporting electrolyte was prepared by dissolving NaCl in deionized water to form a 1 M concentration. The 0.1 M TEMPTMA and 0.1 M MV solutions were prepared by either diluting the 50 w/w % TEMPTMA solution or MV powder in the prepared 1 M NaCl supporting electrolyte solution. Volume changes caused by TEMPTMA and MV content were considered to be negligible.
All battery experiments as well as the data acquisition for the Open Circuit Voltage (OCV) cell 5 were conducted in a glovebox using a VSP potentiostat/galvanostat (Bio-Logic, France). The used RFB cells were custom-made flow-through cells using graphite current collectors, GFA-6 felts (SGL, Germany) and Fumasep FAA-3-50 anion exchange membranes (fumatech GmbH, Germany) with an effective membrane area of 5 cm². As OCV cell, a custom-made two compartment electrochemical cell using a Fumasep FAM anion-exchange membrane as a separator and graphite rods as electrodes, was incorporated into electrolyte flow circuit of the non-capacity-limiting compartment. For the OCV sensor calibration, a double fluid circle system was used. A pair of teflon three-way valves was incorporated into the non-capacity-limiting compartment to form two fluid circuits: One, implementing all battery components, namely flow cell, OCV cell, tank; and the second, implementing only flow cell and OCV cell. By means of that it was possible to temporarily establish n-CLC as a limiting compartment and to do cycling in the SOC range from ~0 to ~100%, thereby using full charge-discharge cycles for calibration. Symmetric cell experiments were conducted with a potentiostatic cycling at 0.2 V in either direction with a current cutoff of 2.5 mA (0.5 mA cm −2 ). After several electrochemical cycles, the electrolyte was charged till 50% SOC by time restricted galvanostatic charging at 100 mA with 1.6 V voltage cutoff (although the cutoff was never reached). Then the valves were turned and the fluid circuit excluding the non-capacity-limiting compartment tank was studied. Two full electrochemical cycles were measured at the specified conditions for symmetric cell cycling in this experiment, then the electrolyte was again galvanostatically charged till 50% SOC at 100 mA, subsequently the valves were again turned and symmetric cycling was continued with non-capacity-limiting compartment implementing electrolyte from the tank.
The electrochemical data from the OCV cell (see Figure S1) was fitted in accordance with Nernst equation for one-electron transfer reaction for anolytes: where E [V] represents the measured OCV potential, E 0 [V] is the reference potential of the reference electrolyte, R [J mol −1 K −1 ] is the gas constant, T [K] is the absolute temperature, n is the number of electrons transferred which is 1 for the MV/MVRC redox pair, F [A s mol −1 ] is the Faraday constant, and q(t) [A s] is the amount of capacity loaded into the battery at a time t and q max the maximum total amount of charge loaded in the battery during a half-cycle (either total charge capacity or total discharge capacity).

UV/Vis Spectroscopy and Association Constant Determination
The UV/Vis experiment were conducted in analogy to the report of Geraskina et al.. 16  Prior to the UV/Vis measurements, a reference spectrum from a solution containing 2 mM sodium dithionite in the buffer solution was collected to minimize the signal stemming from the buffer solution and glass cuvette. The UV/Vis spectra of the prepared solutions were measured on a LAMBDA 750 UV/Vis/NIR spectrometer from PerkinElmer (Waltham, Massachusetts). The spectra were recorded between 400 and 1200 nm with a resolution of 4 nm. During the measurement, the lamp and monochromator were switched at 860 nm to achieve maximum sensitivity.
The association constant was determined using a non-linear fitting procedure. 17,18 For this procedure, the absorbance at 864 nm was fitted, as it stems from viologen radical cation dimers 16 using the following equation Where A is the absorbance, C a fitting parameter, K a the association constant and c tot the total viologen concentration. The equation can be derived using the law of mass action and the mass balance according to The recorded UV/Vis spectra and the corresponding non-linear fits can be seen in Figure S26 and                         nm is associated with the formation of viologen radical cation dimers and can be used to determine the association constant between the monomer and its dimer using a non-linear fit (see inset).