# Machine Learning Approaches for Designing Mesoscale Structure of Li-Ion Battery Electrodes

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Simulation Method

#### 2.1. Simulation Scheme

#### 2.2. Generation of Three-Dimensional Virtual Structure of Active Material

^{3}box, until the volume fraction reaches a randomly specified value. The compaction process of the electrode (calendaring) affects the mesoscale structure of the pore region and active material particles. Here, the maximum overlap length, δ, between active material particles is estimated from the compaction pressure P and the number of active material particle, using the theoretical model [21]:

_{ap}indicate the cross-sectional area of the system and the number of particles, respectively. The generated mesoporous structures of the electrode are shown in Figure 2b.

#### 2.3. Estimation of Surface Area of Pore Region and Volume Fraction of Active Material

_{b}, is estimated by the volume fraction of the pore region θ

_{p}to N

_{ap}. The effective volume fraction of the pore region, θ

_{p}

_{,eff}, and the effective surface area, S

_{p}

_{,eff}, are estimated by:

#### 2.4. Simplified Physico-Chemical Model

_{l}and φ

_{l}are the bulk electrolyte conductivity and potential, respectively. The electrolyte resistance, R

_{l}, is estimated from the effective conductivity of electrolyte, σ

_{l}

_{,eff}, by:

_{reac}, between the active material and the electrolyte is evaluated by the linearized Butler–Volmer equation:

_{0}, i, η, α, F, R, and T denote the exchange current density, current density per surface area of active material overpotential, transfer coefficient, Faraday constant, gas constant, and temperature, respectively. I and L are the current density per cross section and system length, respectively.

_{s}, by:

_{s}indicates the Li concentration in the active material. In this study, Equation (10) is simplified assuming a single spherical particle:

_{s}is the concentration polarization. Therefore, the Li diffusion resistance can be estimated as:

_{0}, and the open circuit voltage (OCV) function:

_{max}is the coefficient of maximum Li concentration of the active material, p

_{i}indicates the coefficient of the polynomial OCV function given in Table 1. These simplifications make it possible to reduce the calculation load for three-dimensional complex structures.

_{tot}, of the electrode is evaluated by the summation of the electrolyte resistance, R

_{l}, the reaction resistance, R

_{reac}, between the active material and the electrolyte, and the Li diffusion resistance, R

_{diff}:

_{1/3}Mn

_{1/3}Co

_{1/3})O

_{2}) positive electrode (an oxide material) are employed, as shown in Table 2.

#### 2.5. Machine Learning Model

^{2}value.

## 3. Results and Discussion

#### 3.1. Sensitivity Analysis of Each Specific Resistance

#### 3.2. Neural Network Regression

^{2}, for the validation data are listed in Table 4. The R

^{2}values for ANNs that consist of two hidden layers are higher than the ones that consist of a single layer. The values saturate around 16 neurons.

#### 3.3. Process Parameters Optimized by Bayesian Optimization

#### 3.4. Optimized Process Parameters in Higher Capacity

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Flowchart for the generation of the artificial structure with controllable process parameters, and (

**b**) the generated mesoporous structures of the electrode (50 × 50 × 50 µm

^{3}).

**Figure 3.**Sensitivities of (

**a**) reaction resistance, (

**b**) electrolyte resistance, (

**c**) Li diffusion resistance, and (

**d**) total specific resistance to the volume ratio of the active material, with a total of 2100 simulation results.

**Figure 4.**Sensitivities of (

**a**) reaction resistance, (

**b**) electrolyte resistance, (

**c**) Li diffusion resistance, and (

**d**) total specific resistance to the radius of the active material, with a total of 2100 simulation results.

**Figure 5.**Sensitivities of (

**a**) reaction resistance, (

**b**) electrolyte resistance, (

**c**) Li diffusion resistance, and (

**d**) total specific resistance to the pressure, with a total of 2100 simulation results.

**Figure 6.**Sensitivities of (

**a**) reaction resistance, (

**b**) electrolyte resistance, (

**c**) Li diffusion resistance, and (

**d**) total specific resistance to the binder/additives volume ratio, with a total of 2100 simulation results.

**Figure 7.**Scatter plots between the specific resistances calculated by the simplified physico-chemical models and predicted by various artificial neural network (ANN) models with training data and test data.

**Figure 8.**Comparison of summations of the weight coefficient magnitudes of the first layer neurons for various design parameters.

**Figure 10.**(

**a**) Packing structure of the active material particles (50 × 50 × 50 µm

^{3}), and (

**b**) radar chart of each specific resistance factor in the condition of the optimized process parameters.

**Figure 11.**Dependence to the volume ratio in the active material of (

**a**) total specific resistance, (

**b**) pressure in the compaction process, (

**c**) active material radius, and (

**d**) binder/additives volume ratio.

**Table 1.**Coefficients of the polynomial open circuit voltage (OCV) function [11].

Coefficient | Value |
---|---|

p_{6} | −43.8299 |

p_{5} | 109.273 |

p_{4} | −99.9523 |

p_{3} | 39.8270 |

p_{2} | −5.52739 |

p_{1} | −1.00539 |

p_{0} | 4.19987 |

Parameter | Value | Reference |
---|---|---|

Exchange current density, i_{0} | 0.10 A/m^{2} | Assumed |

Temperature, T | 298 K | Assumed |

Transfer coefficient, α | 0.50 | [8,10] |

Diffusion coefficient in active material, D_{s} | 5.0 × 10^{−13} m^{2}/s | Assumed |

Current density, i | 20 A/m^{2} | Assumed |

Maximum Li concentration of active material, c_{max} | 36,224 mol/m^{3} | [17] |

# | Descriptors | Predictors | ||||||
---|---|---|---|---|---|---|---|---|

Active Material | Binder/Additives | Electrolyte | Compaction Process | Reaction Resistance (Ω·m) | Electrolyte Resistance (Ω·m) | Diffusion Resistance (Ω·m) | ||

Volume Fraction (%) | Radius (µm) | Volume Ratio (%) | Conductivity (S/m) | Pressure (MPa) | ||||

1 | 77.8 | 10.5 | 28.5 | 0.77 | 3.12 | 1.03 | 291 | 9.68 |

2 | 85.4 | 11.5 | 0.254 | 0.35 | 23.2 | 1.71 | 20.4 | 4.02 |

… | … | … | … | … | … | … | ||

2100 | 85.4 | 11.5 | 0.852 | 0.35 | 14.6 | 1.75 | 80.7 | 2.49 |

Number of Hidden Layers | Number of Neurons | |||||||
---|---|---|---|---|---|---|---|---|

2 | 4 | 6 | 8 | 10 | 12 | 16 | 20 | |

1 | 0.326 | 0.788 | 0.834 | 0.810 | 0.790 | 0.978 | 0.937 | 0.979 |

2 | 0.330 | 0.795 | 0.822 | 0.863 | 0.827 | 0.845 | 0.990 | 0.990 |

Active Material | Binder/Additives | Electrolyte | Compaction | |
---|---|---|---|---|

Volume Fraction (%) | Radius (µm) | Volume Ratio (%) | Conductivity (S/m) | Pressure (MPa) |

50.4 | 6.00 | 0.0820 | 1.00 | 590 |

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**MDPI and ACS Style**

Takagishi, Y.; Yamanaka, T.; Yamaue, T.
Machine Learning Approaches for Designing Mesoscale Structure of Li-Ion Battery Electrodes. *Batteries* **2019**, *5*, 54.
https://doi.org/10.3390/batteries5030054

**AMA Style**

Takagishi Y, Yamanaka T, Yamaue T.
Machine Learning Approaches for Designing Mesoscale Structure of Li-Ion Battery Electrodes. *Batteries*. 2019; 5(3):54.
https://doi.org/10.3390/batteries5030054

**Chicago/Turabian Style**

Takagishi, Yoichi, Takumi Yamanaka, and Tatsuya Yamaue.
2019. "Machine Learning Approaches for Designing Mesoscale Structure of Li-Ion Battery Electrodes" *Batteries* 5, no. 3: 54.
https://doi.org/10.3390/batteries5030054