# Influence of Electrode Density on the Performance of Li-Ion Batteries: Experimental and Simulation Results

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## Abstract

**:**

## 1. Introduction

## 2. Battery Cell Manufacturing

#### 2.1. Slurry Preparation: Mixing

#### 2.2. Coating and Drying

#### 2.3. Calendering

#### 2.4. Cutting/Slitter/Puncher

#### 2.5. Assembly

#### 2.6. Electrolyte Injection, Formation and Wetting

- Particle size and distribution
- Relative amount of AM, binder and conductive agent in the electrode
- Amount of electrode material AM per cm${}^{2}$ current collector
- Thickness and density of the electrode
- Salt concentration of the electrolyte
- Wettability process, determining active area

## 3. Influence of Electrode Density

- Electric conduction at the current collector/electrode interface resulting in a resistive contact impedance. In this regard, it is important to stress the effect of deformation caused by the pressure applied during the calendering procedure. It can be seen that the pressure of the active material on the aluminum current collector deforms this interface creating a better electric contact and thus lower resistance.
- Electric conduction in the matrix of the porous electrode—depending on the intrinsic conductivity of the AM, this electronic current is mostly carried by the carbon-binder domain (CBD) [15].
- Mass transfer (mostly diffusion) of lithium ions in the intercalation host [22].
- The total current passing through the electrode/electrolyte interface is the sum of a capacitive current and faradaic current.
- -
- The capacitive current is due to the electric double layer, formed at the electrode/electrolyte interface. In batteries in general and LIBs specifically, this current is considered to be small relative to the total current [23].
- -
- The faradaic current is due to the charge transfer reaction accompanied with Li-intercalation.

- Ionic conduction in the electrolyte.

#### 3.1. Experimental Part

#### 3.2. Results

**Table 1.**Results of the measurement of the maximum available capacity (MAC) and maximum available energy (MAE) for three cell types.

Measured Quantity | LD | MD | HD | ||||
---|---|---|---|---|---|---|---|

Dis | Cha | Dis | Cha | Dis | Cha | ||

Maximum Available Capacity (Ah/m${}^{2}$) | Mean | 20.81 | 20.82 | 20.84 | 20.87 | 20.84 | 20.87 |

St. dev. | 0.09 | 0.07 | 0.07 | 0.05 | 0.12 | 0.10 | |

Maximum Available Energy (Wh/m${}^{2}$) | Mean | 77.23 | 77.54 | 76.92 | 77.54 | 77.28 | 77.55 |

St. dev. | 0.32 | 0.26 | 0.25 | 0.20 | 0.42 | 0.37 |

**Figure 2.**Influence of the positive electrode density on the discharge capacity at multiple current rates. HD stands for High Density, MD for Middle Density and LD for Low Density. The capacity is given relative to the MAC. The width of the error bars are twice the standard deviation.

**Figure 3.**Influence of the positive electrode density on the Direct Current Resistance at multiple SoC levels. HD stands for High Density and LD for Low Density. The Ohmic cell resisance (or DCR) is given for 1 m${}^{2}$ of positive electrode. The width of the error bars equals two times the standard deviation.

#### 3.3. Discussion

## 4. Model Validation

**Table 2.**Porous electrode theory (PET) model of Li-ion battery [20].

Domain | Equations | Boundary Conditions |
---|---|---|

Electrodes | $\frac{\partial {c}_{s}}{\partial t}=\frac{1}{{r}^{2}}\frac{\partial}{\partial r}{r}^{2}{D}_{s}\frac{\partial {c}_{s}}{\partial r}$ | ${D}_{s}\frac{\partial {c}_{s}}{\partial r}=-{j}_{i}$ at the electrode-electrolyte interface |

$\overrightarrow{\nabla}\xb7{\sigma}_{eff}\overrightarrow{\nabla}{\Phi}_{s}=0$ | ${\sigma}_{eff}\overrightarrow{\nabla}{\overline{\Phi}}_{s}\xb7{\overrightarrow{1}}_{n}=-I$ at current collectors | |

${\sigma}_{eff}\overrightarrow{\nabla}{\overline{\Phi}}_{s}\xb7{\overrightarrow{1}}_{n}=-aF{j}_{i}$ at the electrode-electrolyte interface | ||

Electrolyte | $\u03f5\frac{\partial {\overline{c}}_{e}}{\partial t}=\overrightarrow{\nabla}\xb7{\tilde{D}}_{\mathrm{eff}}\overrightarrow{\nabla}{\overline{c}}_{e}+\overrightarrow{\nabla}\xb7\frac{{\omega}_{+,\mathrm{eff}}}{{\nu}_{+}}\overrightarrow{\nabla}{\overline{\Phi}}_{e}$ | ${\overrightarrow{J}}_{+}\xb7{\overrightarrow{1}}_{n}=\frac{a}{{\nu}_{+}}{j}_{i}$ at the electrode-electrolyte interface |

$\overrightarrow{\nabla}\xb7{\kappa}_{\mathrm{eff}}\overrightarrow{\nabla}{\overline{\Phi}}_{e}+\overrightarrow{\nabla}\xb7{\gamma}_{\mathrm{eff}}\overrightarrow{\nabla}{\overline{c}}_{e}$ = 0 | ${\overrightarrow{J}}_{Q}\xb7{\overrightarrow{1}}_{n}=aF{j}_{i}$ at the electrode/electrolyte interface |

**Figure 5.**Discharge capacity at multiple current rates relative to the MAC for three different cell designs: from low to high PE density. The three dashed curves are predictions based on simulation results, the full lines are experimental results.

**Table 3.**Material and cell design parameters of the positive electrode which change for the different cell design.

Parameter | Symbol (Unit) | LD | MD | HD |
---|---|---|---|---|

Electrode thickness | δ (μm) | 52.0 | 48.5 | 46.0 |

Volume fraction of electrolyte | ${\u03f5}_{e}$ | 0.321 | 0.272 | 0.233 |

Electric conductivity | ${\sigma}_{i}$ (S/m) | 1.00 | 0.60 | 0.20 |

## 5. Conclusions

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Smekens, J.; Gopalakrishnan, R.; Steen, N.V.d.; Omar, N.; Hegazy, O.; Hubin, A.; Van Mierlo, J.
Influence of Electrode Density on the Performance of Li-Ion Batteries: Experimental and Simulation Results. *Energies* **2016**, *9*, 104.
https://doi.org/10.3390/en9020104

**AMA Style**

Smekens J, Gopalakrishnan R, Steen NVd, Omar N, Hegazy O, Hubin A, Van Mierlo J.
Influence of Electrode Density on the Performance of Li-Ion Batteries: Experimental and Simulation Results. *Energies*. 2016; 9(2):104.
https://doi.org/10.3390/en9020104

**Chicago/Turabian Style**

Smekens, Jelle, Rahul Gopalakrishnan, Nils Van den Steen, Noshin Omar, Omar Hegazy, Annick Hubin, and Joeri Van Mierlo.
2016. "Influence of Electrode Density on the Performance of Li-Ion Batteries: Experimental and Simulation Results" *Energies* 9, no. 2: 104.
https://doi.org/10.3390/en9020104