Characterising lithium-ion electrolytes via operando Raman microspectroscopy

Knowledge of electrolyte transport and thermodynamic properties in Li-ion and beyond Li-ion technologies is vital for their continued development and success. Here, we present a method for fully characterising electrolyte systems. By measuring the electrolyte concentration gradient over time via operando Raman microspectroscopy, in tandem with potentiostatic electrochemical impedance spectroscopy, the Fickian “apparent” diffusion coefficient, transference number, thermodynamic factor, ionic conductivity and resistance of charge-transfer were quantified within a single experimental setup. Using lithium bis(fluorosulfonyl)imide (LiFSI) in tetraglyme (G4) as a model system, our study provides a visualisation of the electrolyte concentration gradient; a method for determining key electrolyte properties, and a necessary technique for correlating bulk intermolecular electrolyte structure with the described transport and thermodynamic properties.


Supplementary Method 1. Densitometry
Preparing concentrations on a gravimetric scale is more accurate than volumetric, as one uses an analytical balance instead of relying on the accuracy a volumetric flask. To accurately convert to a volumetric scale (molality to molarity), high precision 5-digit density measurements were run using an Anton Paar DMA 4100 density meter, located in an Argon-filled glovebox. Each measurement was temperature controlled at 20 o C, because this was the operation temperature of the Raman microscope. The density meter was rinsed with isopropanol (>=99.9%, HPLC grade, Fisher Chemical) at least three times and dried in ambient argon between measurements. The density curve is presented in Supplementary Figure 1a.

Supplementary Method 2. Partial Molar Volumes
The partial molar volumes of the salt ( ) and the solvent ( 0 ) were calculated from the density and its dependence on electrolyte concentration using equations [1]: Where 0 and were the molar masses of the electrolyte (222.3 −1 ) and the salt (187.1 −1 ) respectively. Using the density curve data:   Figure 3: a) Concentration gradient comparison between the cells placed vertically and horizontally, after current was applied for 12 h at 100 µA cm −2 . If placed horizontal, the gradient suffers from natural convection due to the density gradient. b) Diagram showing annular flow of the electrolyte if the cell was placed horizontally during the experiment. Density gradients that occur perpendicular to the concentration gradient induce natural convection. c) Concentration gradient comparison between cells using currents of 100, 200 and 400 µA cm −2 ; dendrites grew visibly at 400 µA cm −2 d) Example of mossy dendrite formation after applying 400 µA cm −2 over 48 h e) Raman spectra of 1471 cm −1 peak, illustrating the -CH 2 bending/scissoring not shifting over each line scan, indicating the lack of solvent decomposition.

Supplementary Note 1. Fitting Equation
The concentration profile across the cell can be described by the solution to the diffusion equation [2] in the context of a symmetric cell: The boundary conditions used are: Where is the concentration of the electrolyte or salt, , is time, is distance between the electrodes, * is the initial concentration, is the "apparent" Fickian diffusion coefficient, is the applied current density / , and is the number of moles. Equation 7 states the concentration before the experiment is run. Equation 8 states the concentration will equal the initial concentration at increasing distances from the electrode surface. Equation 9 is derived from the constitutive law for cation flux: Where + ( , ) is the cation flux.
Using Laplace transform:¯ Where: And:¯ Inversion then leads to the equation that describes the concentration at the plating side of the cell: Adapting 14 to measure the concentration at the opposite electrode: Where is the distance between the electrodes.
Combining the two equations allows one to look at the concentration at both sides of the cell: Equation 16 can be simplified so that only two parameters are included, a and b: Where: For equation 17 to remain valid, 2( ) In other words, the diffusion layer cannot extend into the centre of the cell for equation 16 to remain valid. Due to the large that was used experimentally, the equation still held for our experiments.

Supplementary Note 2. Error Estimation Summary
Presented is a summary for each parameter's calculation and error estimation. For most of our calculations when propagating error we used the multiplication/division error propagation equation 20. We will note if we use a different equation when performing propagation with other functions.  vs. ln , = , =0 . The y-axis error was calculated with 0 + and the x-axis had error in measuring the interfacial concentration ratio. The error in ln , = , =0 ( ) was determined from the average interfacial concentration ratio ( , = , =0 ), which was calculated from the fitting equation (equation 1-main text), and its standard error ( ). This allowed the use of the error propagation equation when using natural log: was subsequently calculated from linearly fitting 2 (1− 0 vs. ln , = , =0 , weighted by x and y error. and error was calculated from the standard deviation of four R measurements prior to cell polarisation. With the distance and area known very accurately, is very small, and not noticeable in Figure 4a in the main text. A zoomed version of the fitting is included, highlighting the small amount of error for this measurement. For the Stefan-Maxwell diffusion coefficients ( , 0+ , 0− , −+ ), error was calculated by propagating and error.

Supplementary Note 3. PEIS
To compare PEIS at each concentration, Supplementary Figure 4 shows the fittings of each PEIS spectrum after 4 h rest, for and measurement. The fitting used is described in the main text. The equation proposed by Casteel and Amis was used to fit the trend of vs. concentration: Where 1 and 2 are constants, is the concentration at the maximum ionic conductivity, .

Supplementary Note 4. Concentration Profiles
Shown in Supplementary Figure 5a is a series of selected-area Raman spectra, focusing on the normalised FSI − 717 cm −1 peak. Plotted is the evolution of peak shape and intensity from the plating to the stripping electrode, highlighting changes in electrolyte environment. By monitoring the 717 cm −1 peak, one notices the shape and composition of the gradient that is forming. At positions closer to the stripping electrode, the shoulder peak at 720-750 cm −1 is more noticeable owing to the evolution of contact ion pairs (CIPs) and aggregates (AGGs),

Supplementary Note 5. Diffusion Coefficients
To check the reliability of our measurement, was compared to the often-used restricteddiffusion method in the literature. [3] Using a restricted-diffusion cell and following the relaxation from an arbitrarily formed concentration gradient, the OCV decay can be followed with time, and using equation 23 below, was calculated. The OCV curve eventually becomes linear after enough time has elapsed, and the resulting slope is proportional to .
In this work, the same cell was used: a quartz-glass tube between two stainless steel pistons, but a shorter tube was cut so that the time for OCV relaxation was reduced. The distance between the electrodes, , was 6.58 mm, accurately measured by the optical microscope. Crucially for this experiment has to be small enough so that can be measured in a reasonable time. By plotting ln(OCV) vs. time, the diffusion coefficient was calculated to be 6.98 × 10 −11 m 2 s −1 .
The results from the relaxation are shown in Supplementary Figure 6d.

Supplementary Note 6. Transference Number
Analogous to the Hittorf method, [3] we checked 0 + by measuring the concentration difference between each side of the cell after a molar amount of charge passed, illustrated in Supplementary  Figure 7 and equation 25 below. Specifically, we measured the electrolyte molar difference between each side of the cell, which was done by integrating the measured 1D concentration gradient, and then multiplying it by the cross-sectional area of the cell. This assumes the uniform concentration in the x-and y-directions of the cell.
Where ℎ is the number of moles of charge passed, is the molar difference between the two sides of the cell before and after time, , is the charge passed over time, is the area of the electrode and is the concentration change within the blue shaded area. The (1 − ) factor accounts for bulk diffusion as described by Monroe et al. [3] As can be noted from Supplementary Figure 7, 1 does not have to be the initial concentration before current has passed, like that performed for traditional Hittorf measurements.

Supplementary Note 7. Thermodynamic Factor
Supplementary Figure 8a shows how the voltage changed as current passed in the 1m LiFSI in G4 model cell, with Supplementary Figure 8b illustrating how R + R stayed quite constant throughout the experiment. This indicated that the increase in voltage was only due to the concentration gradient formation. Supplementary Figure 8c shows how concentration at each cell extreme was progressing throughout the experiment.
For higher concentrations (¿0.5m) ohmic and charge transfer resistances were very steady throughout the experiment. This meant the increasing overpotential was due only to the increasing concentration difference on either side of the cell, with no changes to the interfacial resistance. For lower concentrations (¡0.5 m) PEIS showed an increase in ohmic resistance as the concentration approached zero on the plating side. It would appear that at these concentrations the distribution of + ions are non-uniform. It was therefore especially important to perform PEIS throughout the experiment at low concentrations to accurately determine the concentration overpotential. Figure  S8d, illustrating the values extracted from the different gradients.

Fittings of equation 4 (main text) for each concentration were plotted in Supplementary
As mentioned in the main text, vs. concentration was fitted using 1/2 power series, analogous to the Guggenheim extended Debye-Huckel theory. [4] Debye and Huckel developed a theory to describe only how ion association can influence activity values, [5] but with an incomplete picture, multiple variations of their formulation were established. [6,7] Activity's dependence on the square-root of composition can be noted from the Debye-Huckel equation: Where ± is the activity coefficient. The fraction on the right-hand side is from classical Debye-Huckel theory, where is the molar ionic strength, and are coefficients informing the extent of association. is an additional linear factor that accounts for short-range solvent-ion effects, and the primary basis for extended Debye-Huckel theories. With difficulty fitting curves with equation 26, most non-aqueous electrolyte used a 1/2 power series as suggested by Guggenheim.  Table 2 shows how the solvation number is changing with concentration. Clearly, as concentration increases the solvation number decreases due to the availability of solvent molecules with increasing concentration. The increasing amount of bound solvent as the [Li(G4)] + complex would lead to an increase in . Supplementary

Supplementary Note 8. Stefan-Maxwell Diffusion Coefficients
Most articles that rigorously characterise electrolytes base their characterisation on concentratedsolution theory, outlined by Newman and Thomas-Alyea. [3,10,11] Using Stefan-Maxwell theory it is the electrochemical potential gradient which is the driving force that induces diffusion. As stated by Rehfeldt et al., Stefan and Maxwell assume an equilibrium of thermodynamic interaction between the species and molecular friction; if out of equilibrium this leads to flux by diffusion. [12] , derived from Fick's Laws of diffusion, can be defined using concentrated-solution theory [1,10] by equation 28. Where: is the thermodynamic diffusion coefficient, where 0+ and 0− are the Stefan-Maxwell intermolecular diffusion coefficients of the anion or cation and their interaction with the solvent, depending on the subscript.
is the proportionality constant that is influenced by electrochemical potential gradients (thermodynamic driving force) instead of the observed concentration gradients. Where c is the total concentration and c 0 is the concentration of the solvent.
Also, individual Stefan-Maxwell diffusion coefficients based on ion-ion and ion-solvent interactions can be calculated: For a rigorous discussion and derivation of these equations, readers are referred to original work by Newman and Thomas-Alyea. [1,13] Supplementary Discussion 1. Cell Simulations By measuring parameters , 0 + , and one can implement these values into a Doyle-Fuller-Newman (DFN) model and simulate symmetric and full cell performance. We simulated cells using the Batteries and Fuel Cells Module in COMSOL Multiphysics 5.5. Supplementary Figures 9a-c simulate a symmetric cell with a plating and stripping electrode, similar to the cell described in this study, except the interelectrode distances are at 15 µm, 50 µm and 100 µm, and the current density applied is 5 mA cm −2 . In this example, 1m LiFSI G4 was used, with the measured properties from the operando Raman microspectroscopy experiment. Indeed, the measured parameters in this study are independent of current density and interelectrode distance, but it illustrates the extent and speed of concentration gradient formation at more realistic LMB geometries.
Supplementary Figures 9d-f simulate a full LIB cell geometry using porous graphite and porous lithium manganese oxide (LMO) as the negative and positive electrode respectively. Full cell parameters are described in the table below. Supplementary Figure 9d shows a galvanostatic discharge curve at a 1C C-rate, illustrating how electrolyte concentration, transport and thermodynamic properties can influence the shape of the curve, and ultimately overall cell performance. Interestingly, it is 1m and 0.5m that performs best, showing the least overpotential. Supplementary  Figure 9f shows how the concentration gradient of the electrolyte progresses over 1h. Supplementary Figure 9e highlights even further how electrolyte composition can influence cell performance, when increasing the C-rate to 4C. The biggest influencer on final state-of-charge (SOC) is the bulk concentration, with 0.25m and 0.5m performing particularly poorly. Supplementary Figure 10a-b shows the difference in electrolyte concentration distribution for the 0.5m electrolyte discharged at 1C and 4C respectively. Due to the low initial concentration throughout the cell and a high C-rate causing large concentration gradients, the concentration in the cathode drops to zero in much of the electrode. This leads to a low final average SOC at a 3V cut-off.
But, again it is 1 m that achieves the best results, showing the least overpotential and highest final capacity at a 3 V cut-off.
A 1D model was used to simulate each setup. For the symmetric cell, distances of 15 µm, 50 µm and 100 µm between two nodes were used. For the full cell, graphite and LMO were implemented, Li C 6 -electrolyte-Li Mn 2 O 4 . The graphite thickness was 100 µm, the electrolyte 50 µm and LMO was 185 µm. others in the field have utilised this model to understand how parameters such as transference number may affect cell performance. [15] Symmetric Cell The DFN model combines concentrated solution theory to account for electrolyte flux in non-ideal solutions, and porous electrode theory to understand behaviour in porous microstructures.
Molar flux in a binary electrolyte is governed by:  Where is the molar flux of i, is the Faraday constant and is the current density of i and . To know current density, one needs to understand how electrolyte potential is varying in solution: Where Φ is measured with a lithium reference electrode, is the temperature, is the ideal gas constant.
In short, equations 33 and 35 describe how electrolyte potential and concentration vary in an electrolyte. Then, one needs to set the boundary conditions. At one boundary (x=0), the potential is set to zero, and the other (x=L) includes the flux of lithium ions: An applied current of 5 mA cm −2 was used in our simulations.
To measure how current at the interface influences surface overpotential, the Butler-Volmer equation was used: is the local current density at the interface, is the local activation overpotential, is the anodic and cathodic transfer coefficients and 0 is the exchange current density. 0 was assumed to be 1 A/m 2 .

Full Cell
Full cell simulations utilised the equations above to describe electrolyte concentration and potential, and reaction kinetics at the interface. But further to this, porous electrode theory was used.
For full cell simulations the porous electrode consisted of spherical active material particles and LiFSI in G4 electrolyte in the void space. The electric current in the active material particles was defined by Ohm's Law: Where is the electric conductivity of the material.
With the full cell consisting of insertion electrodes, Li + diffusion was defined by Fick's Law: Where is the diffusion coefficient of Li + in the material, and is the concentration of lithium in the solid phase.
The interfacial kinetics were again defined by equation 36 with 0 defined as: Where is the rate constant and is the solid phase lithium concentration.
The current density was specified at the cathode/current collector interface.