Operando and three-dimensional visualization of anion depletion and lithium growth by stimulated Raman scattering microscopy

Visualization of ion transport in electrolytes provides fundamental understandings of electrolyte dynamics and electrolyte-electrode interactions. However, this is challenging because existing techniques are hard to capture low ionic concentrations and fast electrolyte dynamics. Here we show that stimulated Raman scattering microscopy offers required resolutions to address a long-lasting question: how does the lithium-ion concentration correlate to uneven lithium deposition? In this study, anions are used to represent lithium ions since their concentrations should not deviate for more than 0.1 mM, even near nanoelectrodes. A three-stage lithium deposition process is uncovered, corresponding to no depletion, partial depletion, and full depletion of lithium ions. Further analysis reveals a feedback mechanism between the lithium dendrite growth and heterogeneity of local ionic concentration, which can be suppressed by artificial solid electrolyte interphase. This study shows that stimulated Raman scattering microscopy is a powerful tool for the materials and energy field.

When SEI is applied, the heterogeneity of current density on the Li metal surface is greatly alleviated.
The maximum current at lithium surface is reduced from 6.1 mA cm -2 for bare lithium (a) to 2.8 mA cm Fitted / 4.9*10 -7

Supplementary Note 1. Theoretical Analysis on Electroneutrality in the electrolyte
In this paper, the electroneutrality does not mean the difference between [BOB -] and [Li + ] is zero; the difference is small enough to be neglected at given resolutions of SRS microscopy. First, we consider a planar electrode: According to Poisson's Equation for electrostatics, the electrical potential Ф and ionic distribution satisfy: Where F is the Faraday constant (96485 C mol -1 ), ε is the relative permittivity of electrolyte and ε 0 is the vacuum permittivity (8.85×10 -12 F m -1 ), and z i and c i are charge number and concentration of all ions in the electrolyte. In our cell, the maximum voltage is 5 V, and the distance is around 500 μm. Even if we consider an extreme condition, in which the maximum gradient of an electrical field (-▽ 2 Ф) is 5V μm -2 , and relative permittivity is 10, the difference in anion and cation concentration (C + -C -) is still < 5 μM. Therefore, Li + can be reflected by BOBoutside the double layer region (Debye length is 48.7 nm for 5 μM LiBOB) which is much less than our spatial resolution.
Then a nano-electrode was also considered. We performed a simulation of ion distribution in such a Li/Li symmetric cell by Multi-Physics Comsol. The transference number is assumed to be 0.5 for both Li + and anion, the initial concentration is 1 M, the distance between two lithium electrodes is 100 μm, the diffusion coefficient of both Li + and anion is 5*10 -7 cm 2 s -1 , and the current density is 2 mA cm -2 . The electrode is designed to have a single tip with a width of 10 nm and a length of 2 μm. Supplementary Fig. 2 shows the zoom-in image of the tip. In such a cell, when Li + ion is fully depleted at the tip ( Supplementary Fig. 2a), the current density is mainly near the tips (Supplementary Fig. 2b) and the voltage decay more near the tip (Supplementary Fig. 2c).
In this situation, the highest cation-anion concentration difference is observed at the electrode tip, which is still smaller than 0.1 mmol L -1 and can be negligible in our experiment ( Supplementary   Fig. 2d).
Prof. Henry White at University of Utah also analyzed the effectiveness of electroneutrality on microelectrodes 1 Where r o is the radius of spherical microelectrode, F is the Faraday constant (96485 C mol -1 ), ε is the relative permittivity (ε=7.8 for TEGDME) 2  Therefore, the maximum charge difference occurs at γ = 0, which means no supporting electrolyte to shield electrical field. This is also the same as our experimental condition, where the electrolyte is binary without supporting electrolyte (γ = 0). In this case, the second term in the square brackets is zero, and the equation can be simplified to 2 2 18.4(

Based on supplementary equation 3, the difference between [Li + ] and [BOB -] is purely
determined by the distance to the center of the microelectrode. Therefore, r could be much smaller in microelectrode than the bulk electrode. Even if the electrode size is 10 nm, and we measure 100 nm away from the electrode/electrolyte interface, c +c -= 18.4 / (110 2 ) = 1.52 × 10 -3 mM , which is much less than SRS resolution. Besides, the typical Debye length is ~ 5 nm at the concentration of 1 mM, so 100 nm satisfy the prerequisite of outside Debye region.

Supplementary Note 2. Experimental Analysis on Electroneutrality in the electrolyte
As the SRS setup at Columbia can only detect wavenumber higher than 1000 cm -1 , we cannot directly see Li + ion based on Li-electrolyte interaction. Therefore, we track both Li + and BOBnear the electrode surface by spontaneous Raman to derive their local concentration. The electrolyte used in this experiment is LiBOB / (TEGDME: EC v/ 7:3) instead of LiBOB / TEGDME, so that [Li + ] can be tracked by the Li + -EC interaction at 725 cm -1 , and BOB at 1830 cm -1 (Fig. 2a).
As shown in the inset of During the cell operation, lithium is deposited as dendrite and gradually approach the Raman spot which has a size ~10 μm. We find that when the laser directly shines at lithium, severe signal loss and distortion will occur, which may be due to interactions with SEI and lithium. Therefore, we only approach ~ 10 μm away from the lithium surface, which is similar to our paper (Fig. 2c).
After converting Raman intensity to ion concentration, we can see that [Li + ] and [BOB -] are reduced due to ion depletion ( Supplementary Fig. 3b & Fig. 2d). Their absolute concentrations synchronize with each other so that they appear to be the same as each other and electroneutrality is valid.
To further answer this question more quantitatively, we performed the hypothesis testing in statistics. Data at 50 minutes were used as an example here. For cations LiBOB/TEGDME, LiTFSI/TEGDME, and LiTFSI/ DMC up to high concentrations ( Supplementary   Fig. 4). In LiBOB/TEGDME, it is 0-0.5 M as the solubility is ~ 0.7 M, and it is 0-2 M for LiTFSI in TEGDME or DMC. The Raman intensity is for a given wavenumber instead of peak integration, to make it consistent with SRS measurement. Both correlation coefficients are higher than 0.999.
We indeed need to identify these modes, to see whether CIP/AGG is involved, but no matter whether it is for free or with interaction, experimental Raman signal is linear with anion concentration in a reasonable range for battery electrolyte, as shown in Supplementary Fig. 4.
Second, strong interaction to cause nonlinearity only occurs for really high concentration, which is not common in battery systems 3 , and we are studying low ion concentration in depletion, so linearity should be general in this range. Third, the Raman intensity of direct Li + -solvent interaction is linear with Li + concentration as shown in Fig. 2a, the intensities of Li + -EC have excellent linearity with Li + concentration.
Therefore, the salt-solvent will not generate deviation in SRS experiments.
In the current configuration, the Stokes laser is fixed at 1064 nm, and a pump laser could be tuned in principle from 720 to 990 nm (corresponding to 700 -4500 cm -1 ). Due to the currently optimized stability for OPO tuning, the optimal detection window ranges from 1000 to 3300 cm -1 .
Therefore, BOB -(1830 cm -1 ) is chosen over PF 6 -(770 cm -1 ) 4 and Li-propylene carbonate (721 cm -1 ) 5 . The detection range can be expanded by further optimizing the OPO cavity to stabilize the tuning range around 700 cm -1 for monitoring the counter ions as mentioned above.
The detection limit is determined from the concentration curve shown as the inset of Fig. 1d when the SRS signal-to-noise ratio equals to 1. The signal is linearly extrapolated from concentration curve, while the noise is read from the standard deviation of pump-only SRS image.
Such noise level in our experiment is approaching the laser shot-noise level. The ionic concentration limit is finally determined to be 10 mM. Dwell time: 2 μs per pixel, 16-time frame average. Power: P pump = 24 mW and P pump = 50 mW on sample.

Supplementary Note 6. Simulation
The simulation follows previous Newman's model 6 . The transport of lithium ion can be solved by 1D Nernst-Planck equation: In this equation, N i is the flux density of species i; z i F is the charge per mole on the species.
D i and μ i are the diffusion coefficient and migration coefficient of species i, respectively. The first term on the right side represents the ionic flux under the electrical field; the second term represents the diffusion current. Convection is neglected since the gel immobilizes the electrolyte.
By combining Nernst equation of both Li + and BOB -, and cancelling the migration term, the ion transport behavior can be reduced to and the boundary conditions are: j is the current density applied to the cell, and L is the distance between two lithium electrodes.
This equation is used to fit experimental results in Fig. 3 and the results are labeled as red lines in Fig. 3g. D is simulated based on least squares estimator. Here t + is assumed as 0.5 for convenienc 7,8 . The details can be found in chapter 11 of Electrochemical Systems authored by Prof. John Newman 6 .
The effective ionic mobility based on experimental ionic conductivity and ion concentration according to the equation Where σ is the conductivity of gel electrolyte obtained from Electrochemical Impedance Spectroscopy (EIS) measurements. μ is the ionic mobility. z i is +1 for Li + , and -1 for BOBwith the assumption that μ + =μ -, μ of Li + can be derived. Then the diffusion coefficient is calculated based on Einstein relation: The data can be found in supplementary table 1.

Supplementary Note 8. Current stepping test
Current stepping test further confirms the ion depletion-driven dendritic growth in a different Li/Li cell (Supplementary Video 2 & Supplementary Fig.11). When 0.6 mA cm -2 is applied, which is smaller than limiting current (0.75 mA cm -2 ), the Li + concentration at Li surface is stabilized at 0.1 M after 62 minutes, and the growth rate of Li is also steady (v ave ~ 0.2 μm min -1 ). Once the current is increased to 0.9 mA cm -2 , voltage increases to 2.8 V due to electrolyte resistance and charge transfer overpotential, but still keeps climbing up as a result of depleted ion concentrations.

Supplementary Note 10. Phase-Field Simulation
The Li dendrite morphology evolution and Li-ion diffusion during the selected electrodeposition periods (35-40, 65-70, 100-105 min) were simulated by a phase-field method in two-dimension. A phase-field order parameter, ( ), continuously varying from 1 to 0, was defined spatially to distinguish the Li metal ( = 1) from dilute liquid electrolyte ( = 0) with a finite thickness of diffuse interface at the phase boundary. The diffusion-limited reaction + + − → ( ) takes place at the electrode / electrolyte interface with the assumptions that excess electrons are always supplied at the electrode surface (the activity of electron equals 1).
The phase-field temporal evolution incorporating non-linear Butler-Volmer kinetics follows, is the activation overpotential. + is the local concentration of Lithium ion. is the charge-transfer coefficient ( = 0.5 in this study). , , and are gas constant, the temperature of the system and Faraday's constant, respectively. The Li-ion diffusion is described by Nernst-Plank equation, and the electrostatic potential distribution is governed by Poisson equation, which was coupled and solved together with the phase-field evolution equation (6). The phase field model and Li electrodeposition parametric details are in reference 9, 10 .
All phase-field simulations were performed by COMSOL Multiphysics with finite element meshing. To be consistent with the SRS results, a 320 × 320 μm simulation size with the same electrolyte bulk concentration (0.33 M) and I-V boundary conditions were adopted. The experimental Li dendrite morphologies and Li-ion concentration distribution profiles at 35, 65 and