Supporting Information. Suppressing Dendritic Lithium Formation Using Porous Media in. Lithium Metal Based Batteries

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1 Supporting Information Suppressing Dendritic Lithium Formation Using Porous Media in Lithium Metal Based Batteries Nan Li, Wenfei Wei, Keyu Xie, *, Jinwang Tan,, # Lin Zhang, Xiaodong Luo, Kai Yuan, Qiang Song, Hejun Li, Chao Shen, Emily M. Ryan, Ling Liu and Bingqing Wei*,, State Key Laboratory of Solidification Processing, Center for Nano Energy Materials, School of Materials Science and Engineering, Northwestern Polytechnical University and Shaanxi Joint Laboratory of Graphene (NPU), Xi an , China. Department of Mechanical Engineering, University of Delaware, Newark, DE19716, USA. Department of Mechanical Engineering, Boston University, 110 Cummington Mall, Boston, MA 02215, USA Department of Mechanical and Aerospace Engineering, Utah State University, Logan, UT 84322, USA College of Metallurgical and Materials Engineering, Chongqing University of Science and Technology, Chongqing , China # College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen , China * kyxie@nwpu.edu.cn * weib@udel.edu

2 Parameter Symbol Value Unit Domain length L 16 µm Domain width W 32 µm SPH particle interval µm Diffusion coefficient D 0.25 µm 2 /s Time ~1500 s Concentration 0-1 µmol/µl Equilibrium concentration 0.01 µmol/µl Reaction rate K 5-50 µm/s Table S1. Parameters used in Lagrangian smoothed particle hydrodynamics (SPH) simulations.

3 Solute Dispersion in Nanoporous Media The contribution of molecular diffusion to the spreading of solutes in a porous medium can sometimes be overshadowed by the contribution from the dispersion. For reactive transport of Li + in nanoporous membranes, we performed molecular dynamics simulations to demonstrate that dispersion is not significantly influenced by migration and convection at operating voltages. The simulations employed a model nanoporous material comprised of randomly oriented nanofibers with a uniform diameter of 1.3 nm and a porosity of about 0.8 (Supporting Figure S1a). All fibers were contained in a representative cell of 10 nm 10 nm 10 nm with periodic boundary conditions applied along all directions. Fibers were made rigid (non-deformable) and continuous across cell boundaries. Space between the fibers was filled with 1.0 M LiTFSI in DME:DOL=1:1 vol% without the addition of LiNO 3 (Supporting Figure S1b). Molecular transport of the electrolyte in this porous environment was simulated by using the OPLS-AA force field. Non-bonded interactions between different types of atoms were determined by the geometric mixing rule. Long-range Coulomb s interactions were captured by using the particle-particle particle-mesh method (PPPM) with a root mean square accuracy of Spreading of Li + was calculated by = 1 6 lim 0 where is the apparent diffusion coefficient, is the ion position at time, the angle brackets denote an average over the entire ion group, and 0 means the ion mean squared displacement (MSD). In equilibrium state, the MSD of a

4 particle should grow linearly with time, based on which can be determined. Simulations were performed assuming zero voltage and a voltage of 1 V across the cell. Results of the MSD in both cases are plotted in Supporting Figure S1c. The two curves almost overlap, giving almost the same diffusivity of cm 2 /s implying insignificant effects of migration and convection on dispersion. Note that the voltage applied in this simulation is larger than realistic values, so the effects may be even smaller in actual systems. Figure S1. Molecular transport simulation. (a) A model porous medium. (b) The computational model of an electrolyte filling pores between fibers (red: Li + ; brown: TFSI - ; green: DME; grey: DOL). (c) Spreading of Li + with time.

5 Figure S2. Dendrite growth simulation results with a reduced membrane porosity at t = 1500 s. (a) The reaction rate of K = 50 µm s -1. (b) The reaction rate of K = 5 µm s -1. Both the two suppression effects can be reduced in less tortuous and wider pores. Here, the porous membrane was modeled with a decreased porosity of 0.34 (10% less) and a reduced tortuosity. Computational results show more and longer dendrites formed in the system (Supporting Figure S2), indicating reduced suppression effects in less porous and tortuous membranes. However, despite the changes in geometry, the two suppression effects of the porous membrane on impeding dendrite formation are still preserved.

6 Figure S3. Schematic of the fabrication of the free-standing α-si 3 N 4 submicron-wire membrane. Step 1, the polyurea silazane- and catalyst (Fe)-containing solution is pasted on the carbon fabric. Step 2, after crosslinked at 260 C, the precursor decomposes to amorphous Si-C-N ceramics at about 1000 C. Step 3, the Si-C-N ceramics further react with Fe at ~1300 C to form a liquid alloy. Step 4, at a higher temperature (such as 1500 C), the supersaturated liquid phase reacts with N 2 gas to form Si 3 N 4 submicron-wires at the liquid/gas interface. Step 5, the application of a smooth surface graphite paper on the top of the precursor-containing carbon fiber as a collector. Step 6 and 7, the free-standing Si 3 N 4 submicron-wire membrane is obtained by peeling it off intact from the graphite paper substrate.

7 Figure S4. The typical tensile stress-strain curve of the α-si 3 N 4 submicron-wire membrane.

8 Figure S5. FESEM image of the α-si 3 N 4 submicron-wire membrane.

9 Figure S6. Mercury intrusion porosimetry measurement of α-si 3 N 4 submicron-wire membrane.

10 Figure S7. CV curve of α-si 3 N 4 ǀ Li cell. The as-synthesized Si 3 N 4 is electrochemically inert with Li metal because no redox peak can be found from the CV curve of α-si 3 N 4 Li cell within a wide potential range of 0 to 4.5 V (vs. Li/Li + ).

11 Figure S8. SEM image of the α-si 3 N 4 membrane after Li stripping. (a,c) The top-view and cross-sectional SEM images of Li stripping within the α-si 3 N 4 membrane at a current density of 1.0 ma cm -2. (b,d) Magnified views of a and c, respectively.

12 Figure S9. Cycling performance of the bare Cu current collector and the α-si 3 N 4 -membrane-covered Cu current collector in 1.0 M LiPF 6 in ethylene carbonate (EC)/dimethyl carbonate (DMC) (1:1 in volume) at 1.0 ma cm -2. The deposition capacity of Li is fixed at 1 mah cm -2. As illustrated in this figure, the CE of the bare Cu foil in a carbonate-based electrolyte shows inferior electrochemical performance during the long-term Li deposition and stripping cycles, due to the appearance of Li dendrites. In comparison, the CE of α-si 3 N 4 -membrane-covered Cu foil in a carbonate-based electrolyte presents a more stable cycling life with a nearly constant CE of 95%, due to the homogeneous and dendrite-free Li deposition. These results show that the α-si 3 N 4 -membrane-covered Cu foil has a more stable cycling performance and a longer cycle life than its bare Cu counterpart in an ester electrolyte.

13 Figure S10. Voltage-time curves of Li deposition/stripping in the symmetrical Li Li cell (top) and the Li-α-Si 3 N 4 α-si 3 N 4 -Li cell (bottom) with 1.0 M LiPF 6 in ethylene carbonate (EC)/dimethyl carbonate (DMC) (1:1 in volume). The amount of plated Li is 1.0 mah cm -2, and the current density is 1.0 ma cm -2 in each cycle. The voltage begins to increase after 40 h in the symmetrical Li Li cell, which indicates an internal short circuit due to dendrite growth. However, the voltage-time curve of symmetrical Li-α-Si 3 N 4 α-si 3 N 4 -Li cell shows very stable behavior even after 120h with no sign of a short circuit.

14 Figure S11. Electrochemical performance of the LiFePO 4 Li battery with or without the α-si 3 N 4 membrane. (a) Cycling performance and (b) rate capability of the LiFePO 4 α-si 3 N 4 -Li and LiFePO 4 Li full cells with 1.0 M LiPF 6 in ethylene carbonate (EC)/dimethyl carbonate (DMC) (1:1 in volume). The areal mass loading of the LiFePO 4 cathode was ~10 mg cm -2.

15 Figure S12. Impedance plots of the LiFePO 4 α-si 3 N 4 -Li cell and LiFePO 4 Li cell (a) before cycling and (b) after cycling, respectively. The areal mass loading of the LiFePO 4 cathode was ~4 mg cm -2.

16 Figure S13. Charge/discharge curves of LiFePO 4 α-si 3 N 4 -Li and LiFePO 4 Li full cells with the LiFePO 4 areal mass loading of (a) ~4 mg cm -2 and (b) ~10 mg cm -2.

17 Methods Lagrangian particle method Dendrite growth was simulated near the anode surface by using a two-dimensional Lagrangian particle method applied to the diffusion layer. The framework numerically solves mass, momentum, and species conservation equations using the smoothed particle hydrodynamics (SPH) method for discretization 1. Details of this method can be found in our previous publications 2-4. Simulations were performed under the assumptions that charging current is below the limiting current and dendrite growth is mass transport limited. A first-order precipitation reaction model was adopted to simulate Li + reduction and deposition onto the anode surface:, =,, Γ, >0 where is the diffusion coefficient of Li +, is the Li + concentration, is a unit vector normal to the reactive surface Γ, is the equilibrium concentration of Li + in the reaction, is the reaction coefficient, is a point on the reactive surface Γ, and is time. Outside the diffusion layer, the Li + concentration was set constant and equal to the concentration of Li + in the bulk solution ( ): >, = where L is the thickness of the diffusion layer, and y is the coordinate along the thickness direction. At non-reactive surfaces such as the interface between fiber and the electrolyte, a zero-flux boundary condition was assumed:, =0, Γ, >0 where Γ stands for the non-reactive surface. Initially, at =0, the concentration of

18 Li + was assumed uniform everywhere, equal to. Materials The Li metal was purchased from MTI Corporation. The electrolyte components were purchased from Alfa Aesar and prepared as received in an Argon filled glove box. The separator was Celgard LiFePO 4 was obtained from Henan Long-Time New Energy Co., LTD. Fabrication of Si 3 N 4 The details of the fabrication processes of the free-standing single-crystalline Si 3 N 4 submicron-wire membrane can be found in Supporting Figure S3. Characterizations Transmission electron microscopy (TEM) measurements and X-ray diffraction (XRD) patterns were carried out with Quanta 600 FEG and a X'Pert PRO MPD (Cu Kα radiation, nm), respectively. The morphologies of the samples were observed under a high-resolution transmission electron microscope (HRTEM, FEI Tecnai F30G2). FTIR spectra were collected at 298 K with 1.0 cm -1 resolution using a Nicolet is50 FTIR spectrometer. The mechanical properties were tested on an electronic universal testing machine (CMT 5304, Suns Co. China). The contact angle was measured by an Optical Contact Angle & interface tension meter (SL200KB, Kino, USA), and a 3.0 µl droplet of the ether-based electrolyte was used in the

19 experiment. Electrochemical Measurements CR2016 coin cells were employed for repeated Li deposition/stripping testing. The Li deposition capacity is fixed at 1.0 mah cm -2, and the cut-off potential for the stripping process is configured to be 1.0 V. The electrolyte was 1 M LiTFSI in a mixed solvent of DOL and DME (1:1 in volume) with 2 % LiNO 3. For the symmetrical cell tests, the balanced Li-α-Si 3 N 4 α-si 3 N 4 -Li or Li Li coin cells were assembled in the argon-filled glove box. For the LiFePO 4 full cells, the LiFePO 4 electrodes were prepared by mixing LiFePO 4, polyvinylidene fluoride, and carbon black in the ratio of 8:1:1 with N-methyl-2-pyrrolidone as the solvent. The areal mass loading of the LiFePO 4 electrodes was ~4 mg cm -2. The electrolyte consisted of 1.0 M LiPF 6 in ethylene carbonate (EC)/dimethyl carbonate (DMC) (1:1 in volume). 100 µl of the electrolyte has been added to each coin cell. The masses of α-si 3 N 4 and Li are 4.12 mg and 25.6 mg, respectively. As a result, the mass ratio of α-si 3 N 4 and Li is 1:6.2. And the areal loading of Li in the Si 3 N 4 -Li electrode was 12.7 mg cm -2. All the cells were tested using a CT2001A cell test instrument (LAND Electronic Co, BT2013A, China) or an 88-channel battery tester (Arbin Instruments, BT2000, USA). A Solartron electrochemical workstation ( ) was employed for electrochemical impedance spectrometry tests in the frequency range of 100 khz to 10 mhz.

20 References 1. Monaghan, J. J. Rep. Prog. Phys. 2005, 68, Tan, J.; Tartakovsky, A.M.; Ferris, K.; Ryan, E.M. J. Electrochem. Soc. 2016, 163, A318-A Tan, J.; Ryan, E.M. Int. J. Energy. Res. 2016, 40, Tan, J.; Ryan, E.M. J. Power Sources 2016, 323,