Simulations of Li-ion distribution through separators
This protocol is extracted from research article:
An ion redistributor for dendrite-free lithium metal anodes
Sci Adv, Nov 9, 2018; DOI: 10.1126/sciadv.aat3446

FEM conducted by COMSOL Multiphysics was used to investigate the distribution of Li ions through a routine PP separator and LLZTO composite separator. The migration of Li ions driven by electric field and diffusion flow in both liquid phase (electrolytes) and solid phase (LLZTO particles) was taken into account in these simplified simulations. Two physical models of electrostatic and transport of diluted species based on the partial differential equations listed below were coupled to conduct FEM simulation.Embedded Image(1)Embedded Image(2)Embedded Image(3)where φ is the electric potential, E is the electric field, D is the diffusion coefficient of Li ion, c is the concentration of Li ion, μ is the ionic mobility of Li ion in electrolytes, and N is the flux vector of Li ion. These FEM simulations on the routine PP separator and the LLZTO composite separator were performed in a rectangle area with a size of 30.0 μm by 45.0 μm and 30.0 μm by 50.0 μm, respectively. The routine PP separator was simplified as a sieve plate with a thickness of 25.0 μm, which consists of narrow rectangular channels with a pore size of 1.0 μm and a pore spacing of 1.0 μm (fig. S5). The LLZTO composite separator was simplified as a two-layered sieve plate. The upper layer is the same as the routine PP separator. The under layer with a thickness of 5.0 μm consists of 14 rows of close-packed spherical particles with a particle size of 0.36 μm and a gap of 0.04 μm, which is representing the LLZTO layer (fig. S5). It should be noticed that the sizes in these simulations are representative selected on the basis of the feasibility of FEM modeling and physical sizes according to SEM images (Fig. 2, B and C) and the size distribution of LLZTO. However, this model cannot fully reflect the real circumstance; it can only offer valuable fundamental understandings in ideal systems, since the practical pore structure and pore size distribution are much more complex. In addition, to compare the Li ion distribution near the anode electrode surface after the two transportation behaviors of Li ions through routine PP separator and LLZTO composite separator, the spacing between the electrode and the separator is set to the same distance of 10.0 μm. The potential difference Δφ through these electrolytes is set as 0.02 V. The diffusion coefficients D of Li ions in liquid electrolyte and solid LLZTO particles are set as 3.0 × 10−10 m2 s−1 and 6.0 × 10−12 m2 s−1, respectively. To investigate the ion transport behaviors with limited liquid electrolytes in long-time cycling, the same physical model was established and the ratio of diffusion coefficients of Li ions in liquid electrolytes and solid LLZTO particles was decreased to 10.0. The mobilities of Li ions μ for liquid electrolyte and solid LLZTO particles are defined by the Nernst-Einstein equation. The bottom boundaries of two simulation areas are the Dirichlet boundaries with φ0 = 0 V and c0 = 0 M. The top boundaries of two simulation area are also Dirichlet boundaries with φ1 = 0.02 V and c1 = 1.0 M (fig. S5). The other boundaries are natural boundaries with zero flux.

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