Ion Transport in (Localized) High Concentration Electrolytes for Li-Based Batteries

High concentration electrolytes (HCEs) and localized high concentration electrolytes (LHCEs) have emerged as promising candidates to enable higher energy density Li-ion batteries due to their advantageous interfacial properties that result from their unique solvent structures. Using electrophoretic NMR and electrochemical techniques, we characterize and report full transport properties, including the lithium transference numbers (t+) for electrolytes ranging from the conventional ∼1 M to HCE regimes as well as for LHCE systems. We find that compared to conventional electrolytes, t+ increases for HCEs; however the addition of diluents to LHCEs significantly decreases t+. Viscosity effects alone cannot explain this behavior. Using Onsager transport coefficients calculated from our experiments, we demonstrate that there is more positively correlated cation–cation motion in HCEs as well as fast cation–anion ligand exchange consistent with a concerted ion-hopping mechanism. The addition of diluents to LHCEs results in more anticorrelated motion indicating a disruption of concerted cation-hopping leading to low t+ in LHCEs.


S1.2 Electrolyte Preparation & Physical Characterization
All electrolyte solutions were prepared inside the glovebox using a moles of Li + per kg DMC basis.For electrophoretic NMR measurements of the 1.1m and 2.8m LiFSI in DMC electrolytes PVDF was added (3.4  wt.% and 3.9 wt.% respectively) as a gelling agent to suppress convection.Gelled samples were used only for electrophoretic NMR measurements.Due to their high viscosity, HCEs with concentrations ≥ 5.55m and LHCEs were not gelled with PVDF for eNMR measurements.For electrolytes gelled with PVDF, first the LiFSI was fully dissolved in DMC prior to addition of PVDF.The solution was then rapidly heated to 120 • C while stirring until a clear solution was obtained before the sample was cooled back to room temperature.To prevent LiFSI degradation, high temperature exposure was limited.For LHCEs, the LiFSI was fully dissolved in DMC prior to addition of TTE.We noted that the addition of TTE negatively impacted the solubility of LiFSI in DMC.The solubility limit at 30 • given the 2:1 molar ratio of DMC to TTE was approximately 9.25 mol/kg DMC (1:1.20:0.60 mols Li:DMC:TTE).Solution densities were measured in an Anton Paar DMA 4101 oscillating U-tube density meter at 30 • C inside an argon glovebox.Each density measurement was performed in triplicate.Viscosity measurements were performed in triplicate in an electromagnetically spinning viscometer (EMS-1000s, Kyoto Electronics) spinning at 1000 rotations per minute at 30 • C. Samples were sealed inside air-tight vials inside the glovebox before transfer to the viscometer to ensure no moisture or air contamination.In order to avoid ambiguity in solution concentration definitions, we also report the particle fraction of salt in each solution (y) according to where N i is number of mols of salt (s), solvent (0) and diluent (D) respectively, M i is the molar mass of species 'i', ω i is the mass fraction of species 'i' and ν is the salt stoichiometric coefficient (2 for LiFSI).The salt particle fraction is convenient because y is independent of temperature and pressure and unlike molality does not require a somewhat arbitrary definition of the solvent in mixed solvent systems or micro-phase separated systems (such as the case of localized high concentrated electrolytes). 1

S1.3 Separator Characterization
In order to obtain accurate bulk transport properties for liquid electrolytes measured within a porous separator, it is necessary to know the separator tortuosity (τ ) and porosity (ϵ) or conducting fraction (ϕ c ). Glass fiber separators were chosen over common polypropylene separators (Celgard) due to wetting issues at high concentration.The porosity and conducting fraction of Whatman QMA disks were determined using methods described in ref 2 assuming a density of quartz fiber of 2.2 g/cm 3 .QMA disks were dried for at least 24 hours at 120 • C prior to use.Electrolyte uptake was determined with pure DMC.Tortuosity was measured by comparing the bulk conductivity to conductivity within the QMA separator (κ s ) for aqueous conductivity standards (Mettler Toledo).Conductivity within the QMA separator was measured against blocking stainless steel electrodes in coin cells using AC impedance spectroscopy on a Bio-Logic VMP3 potentiostat in the frequency range from 1 MHz to 100 mHz with a 5 mV AC amplitude.QMA can compress significantly therefore to keep cell thickness constant, QMA disks were set inside a 0.762mm thick PEEK washer prior to loading with 150µL of electrolyte.Impedance data was tested for linearity using a Kramers-Kronig analysis and fit to R-RQ equivalent circuit using the open-source Py-EIS package for Python. 3Conductivity was calculated according to where l is the inter-electrode distance, R hf is the high frequency resistance, and A is the geometric electrode area.Tortuosity was then calculated according to Values for the measured physical properties of our Whatman QMA separators are presented in Table S1.

S1.4 Conductivity
Liquid electrolyte conductivity (κ) was measured using a Mettler Toledo InLab 751-4mm conductivity probe with blocking platinum electrodes inside the glovebox.The conductivity probe was calibrated using 84 µS/cm, 1413 µS/cm, and 12.88 mS/cm aqueous standards (Mettler Toledo) prior to bringing it inside the glovebox.Samples were maintained at 30± • C using a dry block and solution temperatures were verified using the probe's internal sensor.A 5% error is estimated for probe measurements based on replicate measurements.For gelled samples, accurate measurement with the conductivity probe at 30 • C was not possible.Gelled electrolyte conductivity was measured inside a fused electrophoretic NMR cell (P&L Scientific) using AC impedance spectroscopy (Bio-Logic SP-300 potentiostat) in the frequency range of 1MHz to 100 mHz with a 10mV AC amplitude.The cell constant of the NMR cell was measured using 84 µS/cm, 1413 µS/cm, and 12.88 mS/cm aqueous standards.Impedance data was tested for linearity using a Kramers-Kronig analysis and fit to RQ equivalent circuit using the open-source Py-EIS package for Python. 3

S1.5 Restricted Diffusion
Restricted diffusion measurements were performed inside lithium symmetric coin cells.Two QMA disks impregnated with 150µL of electrolyte were set inside a 0.762mm thick PEEK washer and sandwiched between 15 mm brushed lithium electrodes inside a CR2032 coin cell (Hohsen Corporation).Three replicate cells were made for each concentration.Cells were run inside an environmental chamber (Thermotron Inc.) maintained at 30°C and allowed to equilibrate at open circuit potential for 12 hours prior to testing.Cells were polarized at 10 mV for twelve hours to allow concentration gradients to build before allowing the cell to relax at open circuit for twelve hours with potential recorded every 0.5 seconds.5][6] The electrolyte total diffusion coefficient (D ± ) is obtained by multiplying D eff ± by the separator tortuosity.

S1.6 Concentration Cells
Concentration cells were constructed inside a custom fabricated low-volume glass U-cell with a P4 glass frit (Adams & Chittenden).Concentration cell measurements were performed inside the argon glovebox with cell temperature maintained using a dry block with each U-cell equilibrated at 30 • C prior to electrolyte addition.The change in the liquid junction potential across the cell with varied concentration is a function of both the transference number and the electrolyte solution activity.Because we expect t + to vary significantly across concentration, we chose to adopt the "shifting-reference" concentration cell method introduced by Wang et al. 7 For each reference concentration, five concentration combinations were tested with the test concentrations selected to produce reliably measurable liquid junction potentials ∼5 -10 mV without changing the salt:solvent ratio significantly.For the LHCE the upper concentrations were determined by the salt solubility limit.U-cells were constructed using 1mL of electrolyte added on each side of the glass frit before brushed lithium metal wire electrodes were immersed in the solution on each side.The open-circuit potential, U(t), was recorded over the course of 1 hour.Each concentration combination was performed in triplicate.While 3 rd order polynomial fits of concentration cell potential vs. log of salt concentration are often used in the literature, there is no physical reason for this choice, and without sufficient data there can be significant over-fitting.Here, we choose the most parsimonious fit of U (m − m ref ) vs. log(m/m ref ) which in most cases was a linear fit (see Fig. S1).The derivative of concentration cell potential with respect to concentration is then related to the thermodynamic factor (χ) according to distance of 3.35 cm, and an air-tight teflon cap. 8Exact inter-electrode distances were calibrated by measuring the mobility of a 10mM tetramethylammonium bromide solution in deuterated water and comparing to literature values. 8,9Pulsed field gradient (PFG) NMR and eNMR measurement were performed at a field strength of 9.4T on a Bruker NEO 400 MHz spectrometer fitted with a 5 mm water-cooled double resonance broadband diffusion (diffBB) probe equipped with z-axis gradient capabilities up to 17T/m and a variable temperature unit that was maintained at 30 • C throughout measurements.The 90 • pulse time for each peak of interest was measured.Separate 19 F experiments were performed for TTE and FSI peaks due to significant difference in each species 19 F carrier frequency.For PFG measurements, a double stimulated echo bipolar gradient pulse sequence (Bruker pulse sequence diffDSTEAV3) with sin-bell magnetic field gradient pulses (SIN.100) was used in order to eliminate convection-based artifacts for all 3 measured nuclei ( 1 H, 19 F, 7 Li). 10 Eight dummy gradient pulses and sixteen dummy scans were applied at the beginning of each program prior to spectral acquisition to warm up the gradient amps and ensure sample equilibration.For each peak of interest, 16 linearly spaced gradient steps were acquired with the gradient parameters optimized such that the signal attenuates over at least one order of magnitude.PFG data was fit to the Stejskal-Tanner equation where D self i is the self diffusion coefficient of species i, γ is the gyromagnetic ratio, g is the gradient strength including a correction for the sin-bell shape factor, δ is the gradient pulse duration, ∆ is the drift delay, and τ 1 and τ 2 are the gradient recovery delays. 11or eNMR experiments, electric field pulses were applied with a P&L eNMR 1000 electrophoretic highvoltage amplifier unit (P&L Scientific Instrument Services). 8,9eNMR amplifier pulses were controlled by incoming trigger pulses from the Bruker spectrometers to synchronize the electric field pulses with radio frequency (rf) and magnetic field gradient of the eNMR pulse program.Noise from rf pulses was suppressed using a two-stage electronic filter assembly -the first grounded on the NMR preamplifier and the second embedded in the eNMR cell holder provided by P&L.A convection-compensated double stimulated echo eNMR pulse sequence 12,13 was used with bipolar electric field pulses lasting 50 ms each 14,15 to reduce error induced by possible convection, electro-osmotic flow, and bubble formation.eNMR measurements were performed with voltage-controlled electric field pulses with the applied voltage range chosen on a per-sample basis.The lower end of the voltage range was selected such that a phase shift was discernible, ∼ 1 • , while the upper voltage range was selected as the highest voltage before significant signal attenuation due to convection was observed.In order to eliminate any systematic spurious phase shifts that do arise from artifacts, we duplicated each experiment with positive and negative gradient encoding which should result in equal magnitude, but opposite sign phase shifts as a function of applied voltage. 15,16Due to the short-lived nature of electric-field pulses and blocking nature of palladium electrodes, eNMR measurements should not be affected by solution-volume change driven flow (e.g.excluded volume effects or Faradaic convection), 17 or bulk diffusion.Due to the high conductivity and low viscosity of the 1.1m and 2.78m samples, it was not possible to find conditions that did not suffer from significant joule-heating related convective and electroosmotic artifacts.To overcome this, we added a small (∼ 3-4) weight percent PVDF to gel these samples 18 which eliminated most convective artifacts while proportionally lowering the motion of all species by ∼10%.Self diffusion coefficients of the pristine and gelled solutions were compared to ensure that gelling affected all measured species equally.Gelled samples were only used to obtain electrophoretic mobilities and transference number, and all other data presented herein for 1.1m and 2.78m samples are from measurements of pure liquid samples.
eNMR experiments measure ion drift velocities in an electric field which manifests as a phase angle shift in the NMR signal.The phase shift (Φ − Φ 0 ) is directly related to the drift velocity, v and magnetic field gradient parameters according to The electrophoretic mobility of a species i (µ i ) can then be related to the drift velocity at a given the electric field (E) according to To systematically determine the phase of each spectra, we used a modified version of the open source python package eNMRpy to perform phase-sensitive spectral deconvolution assuming Lorentzian line shapes. 16,19,20or each peak fit, we used a matched filter condition such that line broadening matched the natural linewidth of the peak of interest.In order to ensure that our measurements were free of major artifacts, we compared conductivity of our solution obtained by impedance spectroscopy on each sample to those calculated using our measured ion mobilities.Representative values for gradient and voltage parameters used in electrophoretic (eNMR) experiments are listed in Table S2.Exemplary phase shift data vs. g where g is the gradient strength in Tesla per meter, V is the applied voltage in volts, δ is the drift time in seconds, and L is the electrode separation distance in meters.
Velocities from eNMR are all with reference to the stationary NMR probe (v ref = 0).We can switch to a solvent velocity reference frame denoted by a superscript '0' by subtracting the solvent velocity from other species velocities.Here we take the solvent to be DMC for both HCEs and LHCEs.To convert to a center of mass reference frame denoted by a superscript 'COM', we can calculate the center of mass velocity according to where ω i is the mass fraction of species i in the solution.
for three studied nuclei of 1:1.1 molar ratio of LiFSI:DMC (10.1m) high concentration electrolyte. 7Li points correspond to lithium ions in solution and associated with FSI, 19 F points correspond to the FSI anion, and 1 H points correspond to DMC.

S2 Effect of Solution Activity on the Total Salt Diffusion Coefficient
In order to understand if changes in the solution activity coefficient are responsible for differences between the measured total salt diffusion coefficient (D ± ) and the ideal salt diffusion coefficient obtained by the Nernst-Heartly equation (D ideal

S3 Effective Ion Charge
We can calculate an effective ion charge (z eff i ) [21][22][23] by performing a force balance between the Coulombic forces under an electric field and the hydrodynamic friction forces on ions during an eNMR experiment, according to .
We see the cation effective charge increase with increasing molality when from a static picture of ionpairing we would expect more ion pairing and therefore lower effective charge at high concentration (see Fig. S5).This indicates that a static picture of ion-pairing is not appropriate for these systems and that at high concentration effective charge is higher due to shorter lived ion pairs (fast ligand exchange).We observe for the LHCE the effective charge of both the Li + and FSI − ions are reduced, again indicating that the diluent addition impacts ion-solvation dynamics.

S4 Lithium Transference Number Reference Frames
Using electrophoretic NMR we can calculate the transference number with respect to the fixed laboratory reference frame (t Lab + ), center of mass reference frame (t COM + ), or solvent reference frame (t 0 + ).While the solvent reference frame is not particularly meaningful at high salt concentrations, it is frequently used in conventional liquid electrolyte literature and therefore is presented below in Fig. S6.A negative solvent frame transference number does not mean lithium is moving in the "wrong" direction in an electric field, simply that the solvent has a higher electrophoretic mobility than the Li-ion.As discussed in the main text, for HCEs and LHCEs the high apparent solvent mobility is a result of mass conservation in these systems.

)S1. 7
Figure S1: Concentration cell potential vs. log of molality difference.Here the black line represents the concentration cell potential calculated using the Nernst equation (assuming ideal solution behavior).Note: star symbols denote the LHCE of LiFSI in DMC and TTE.Molalities are reported with respect to DMC weight not total solvent (DMC + TTE) weight.

Figure S3 :
Figure S3: Phase shift (degrees) vs. g•V •δ •L −1 (T •s•V •m −2 )for three studied nuclei of 1:1.23:0.62 molar ratio of LiFSI:DMC:TTE (9m) localized high concentration electrolyte.7 Li points correspond to lithium ions in solution and associated with FSI,19 F points in the upper right panel correspond to the FSI anion,19 F points in the lower left panel correspond to the TTE diluent, and 1 H points correspond to DMC.

±)
, we can multiply D ideal ± by the thermodynamic factor (χ).The quantity D ideal ± • χ captures the "ideal" diffusion coefficient with respect to the gradient in solution activity instead of gradients in solution concentration.D ± , D ideal ± , and D ideal ± • χ are plotted versus solution concentration in Figure S4.We observe for all electrolytes except the 10.1m (1.1:1 DMC:LiFSI) HCE that difference the thermodynamic factor is responsible for differences in D ± and D ideal ± .

Figure S4 :
Figure S4: Total salt diffusion coefficients (cm 2 /s) vs. molality (mol Li + /kg DMC) and DMC:Li molar ratio as measured using restricted diffusion and as calculated from PFG NMR assuming ideal solution behavior.Note: star symbols denote LHCE systems composed of LiFSI in DMC and TTE.Molalities are reported with respect to DMC weight not total solvent (DMC + TTE) weight.

Figure S5 :
Figure S5: Effective ion charge vs. molality (mol Li + /kg DMC) and DMC:Li molar ratio.Note: star symbols denote the LHCE of LiFSI in DMC and TTE.Molalities are reported with respect to DMC weight not total solvent (DMC + TTE) weight.

Figure S6 :
Figure S6: Li + transference number with respect to fixed laboratory frame (t Lab + ), center of mass frame (t COM + ), and solvent frame (t 0 + ) vs. molality (mol Li + /kg DMC) and DMC:Li molar ratio as measured by eNMR.Note star symbols denote LHCE systems composed of LiFSI in DMC and TTE

Table S1 :
Measured physical properties of Whatman QMA glass fiber separator