Potentiometric MRI of a Superconcentrated Lithium Electrolyte: Testing the Irreversible Thermodynamics Approach

Superconcentrated electrolytes, being highly thermodynamically nonideal, provide a stringent proving ground for continuum transport theories. Herein, we test an ostensibly complete model of LiPF6 in ethyl-methyl carbonate (EMC) based on the Onsager–Stefan–Maxwell theory from irreversible thermodynamics. We perform synchronous magnetic resonance imaging (MRI) and chronopotentiometry to examine how superconcentrated LiPF6:EMC responds to galvanostatic polarization and open-circuit relaxation. We simulate this experiment using an independently parametrized model with six composition-dependent electrolyte properties, quantified up to saturation. Spectroscopy reveals increasing ion association and solvent coordination with salt concentration. The potentiometric MRI data agree closely with the predicted ion distributions and overpotentials, providing a completely independent validation of the theory. Superconcentrated electrolytes exhibit strong cation–anion interactions and extreme solute-volume effects that mimic elevated lithium transference. Our simulations allow surface overpotentials to be extracted from cell-voltage data to track lithium interfaces. Potentiometric MRI is a powerful tool to illuminate electrolytic transport phenomena.


A. Preparation of LiPF6:EMC solutions
Electrolyte solutions were formulated on a mass fraction basis in a glovebox (Inert Technologies) under argon gas (H2O < 1 ppm, O2 < 1 ppm). LiPF6 salt (99.99%, battery grade, Sigma Aldrich) was dried in a heated vacuum antechamber for 24 hours at 60 ºC, and EMC (99.9%, anhydrous) was dried under 3 Å molecular sieves for a week. Solutions were mixed with magnetic stir bars in polypropylene bottles for over 48 hours to ensure full dissolution. Moisture content was determined by Karl Fischer titration to be below 10 ppm.

B. Ex-situ transport and thermodynamic property characterization
Parameterization of transport and thermodynamic properties followed experimental procedures that have been detailed in previous publications. 1,2 Below we summarize the key methods: Solution densities were measured with a temperature-controlled oscillating densitometer (DMA4100, Anton Paar) within the glovebox. Ionic conductivity was measured with an AC probe (Orion A212, Thermo Scientific) in a sealed, liquid-tight cell placed in a temperaturecontrolled water bath at 25 ºC.
Li-Li coin cells with 2 mm thick annular PEEK spacers were assembled and restricted-diffusion experiments were performed in a 25 °C thermal chamber. 3 The annular gap was packed with a glass fibre separator. Effective Fickian diffusivities were extracted from the voltage decay at open circuit after application of a 100 mV hold for 12 hours, according to , where ε is the separator porosity in the coin cell. Figure S1 shows a representative voltage trace and fitting. The chosen annular spacer thickness and potentiostatic hold ensure a less noisy, longer relaxation period, as discussed earlier by Wang  Custom Hittorf cells with three chambers separated by two valves were used to determine transference numbers, by recording the relative changes in solution density of the anodic and cathodic chambers relative to the central chamber. After passing 14.4 C of charge (Q), both valves were closed and the solution density within each chamber was measured after combing to equilibrium. Hittorf measurements were completed within the glovebox, thermostatted at 25 ºC.
The transference number was calculated from the change in moles (∆ ) of lithium moved relative to the initial bulk concentration (c ∞ ) during the experiment: illustrate an exemplary schematic of the concentration profiles during the Hittorf experiment. Figure S2. (A) Schematic of the valved Hittorf cell with anodic, neutral, and cathodic electrolyte chambers. (B) represents the initial concentration profile, followed by the gradient during polarization depicted in (C) and finally the resting concentrations after current and valves are shut and each chamber is allowed to settle after mixing (D).
Finally, fritted concentration cells with an "H" geometry were used to determine liquid-junction potentials. A matrix of test concentrations was probed using a shifting reference concentration, as described in detail by Wang et al. 1

C. Raman spectroscopy
A Renishaw inVia Reflex laser confocal Raman microscope equipped with a near-IR 785 nm laser and a 5x magnification objective (Leica, 0.12 NA, 14 WD) was used to gather Raman spectra for intermolecular structural characterization. Specifically, full scans were performed from 1600 cm -1 to 700 cm -1 , with a 5% laser power and 10 second exposure time to identify bands of note. Following acquisition, the data was processed using Renishaw WiRE 5.5 software and the background signal was removed. Spectra were then imported into Origin Pro software for further analysis and peak fitting (see supporting discussion S2.E).

D. Potentiometric MRI
The Micro2.5 triple axis gradient system at 298 K, using a water-cooler unit, and 10 mm exchangeable 1 H-19 F/ 7 Li coil. The cell was aligned such the Li metal electrodes were perpendicular to the external magnetic B0-field (and to the z-axis of the gradient).
One-dimensional image profiles were acquired axially (in the z-direction) to get concentration profiles. The image profiles were acquired using the 1D spin-echo sequence (diffprof) reported by Klamor et al. 6

A. Transport model formulation with solute volume effects
The polarization-cell model implemented in COMSOL Multiphysics software follows that outlined by Hou and Monroe. 2 Constitutive laws and balances: Boundary conditions: Initial condition: (S12)

B. Partial molar volume, composition bases, thermodynamic factor
Partial molar volumes for solvent ̅ 0 and solute ̅ plotted on figure 1E are calculated by examining how solution density changes as a function of salt concentration. The following expressions extract partial molar volumes from the density/molarity correlation: 7 (S13) . (S14) Here 0 is the molar mass of EMC (104.105 g/mol) and e is the molar mass of LiPF6 (151.905 g/mol). Electrolytes in parameterization experiments use a variety of composition bases including molarity c, mass fraction , and cation particle fraction y. They may be converted based on the following expressions for binary electrolytic solutions: (S15) . (S16) The thermodynamic factor expresses how the salt's activity in the liquid varies with its concentration. In terms of salt activity coefficients, can be written as , in which m is salt molality and c is salt molarity; +-, +-, and +-respectively represent mean molar salt activity coefficients over particle-fraction, molal, and molar bases.

C. Transport and thermodynamic property correlations
Below is a summary of property correlations used in the transport model, arrived at by following the same fitting procedure described by Wang et al. 1

D. Onsager-Stefan-Maxwell diffusion coefficients
OSM diffusivities for the binary monovalent electrolyte LiPF6:EMC can be mapped from bulk transport properties through (S18) (S19) where D is the thermodynamic diffusivity, equal to the Fickian diffusivity scaled by the thermodynamic factor, / , and Λ is the equivalent conductance, equal to ⁄ .
The extended Stefan-Maxwell equation with electrochemical potential and species velocity ⃗ for species i and j is given by:

E. Raman spectra
Full spectra collected for LiPF6:EMC from 0 M to saturation are plotted in figure S4. It is observed that the scattering efficiency of LiPF6 electrolytes in the super-concentrated regime is poor. 9 Figure S4. Full Raman spectra for LiPF6:EMC at room temperature. Vertically offset for legibility. Figure S5 demonstrates the peak area fitting with Voigt functions in Origin Pro. The neat EMC solvent has a characteristically broad peak at 928 and 937 cm -1 , which is attributed to the free C-O stretching modes influenced by the asymmetric ethyl and methyl groups in EMC. 10 The coordinated solvent peak is seen to emerge at approx. 946 cm -1 , as plotted in figure S5. Figure S5. Stacked Raman spectra in the range of 720 -780 cm -1 for PF6and 920 -980 cm -1 for EMC with peak deconvolution fitting for free (navy) and coordinated (cyan) EMC.
Without prescribing specific speciation for PF6 -, the shifting position of maximum peak height in figure S6 suggests that ion association occurs. It is expected that a quasi-equilibrium exists between solvent-separated ion pairs, contact ion pairs, and higher order aggregates.

Calibration and full MRI profile
Inter-electrode spacing was calibrated with a custom PEEK cell with liquid height of 12 mm.
This separate cell, sealed without electrodes, removes noise introduced by metal susceptibility effects at the interface. 5 Figure S8 compares the overall RF coil signal of a full NMR tube with that of the calibration cell. Additional intensity peaks beyond the bulk electrolyte are residual electrolyte within the threading of the constructed cell, displaced there during cell sealing.

Figure S8
Intensity profile of calibration cell with 12 mm liquid height (red) and overall RF coil signal (black).
Following the attained calibration, the full intensity profile of the MRI cell during the polarization step is also shown below in figure S9.

molar polarization data
To demonstrate validity of the model and parameters for predicting microscopic states across wider ranges of concentration and current density, a repeat experiment was performed with 2 M LiPF6:EMC, using a 2 hour polarization at a current density of 1.9 mA/cm 2 , followed by an open circuit relaxation.   As can be seen in figure S13, the exchange current density during the experiment increases relatively linearly with the square root of time, suggesting surface roughening during electrodeposition. 14 The Butler-Volmer analysis here includes contributions from electrode kinetics and SEI growth. The evolution of interfacial conditions can have a large impact on electrolyte characterization experiments. 15 In the present case, the monotonic decrease in surface overpotential indicates that any growth in interfacial resistance is outcompeted by the increase in surface area from both lithium deposition and SEI formation during the plating process.

I. Other Raw data
Transport and thermodynamic property measurements for LiPF6:EMC were extended from the range studied previously by Wang et al. 1