# Ionic transport properties in solid polymer electrolytes: in-plane versus through-plane

Roselyne Jeanne-Brou, Jonathan Deseure, Didier Devaux, R. Bouchet

► To cite this version:

Roselyne Jeanne-Brou, Jonathan Deseure, Didier Devaux, R. Bouchet. Ionic transport properties in solid polymer electrolytes: in-plane versus through-plane. Journée Scientifique PEM - ED, Oct 2021, Grenoble, France. hal-03793928

HAL Id: hal-03793928

https://hal.science/hal-03793928

Submitted on 2 Oct 2022

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Ionic transport properties in solid polymer electrolytes: in-plane versus through-plane

Roselyne Jeanne-Brou, Jonathan Desseure, Renaud Bouchet, Didier Devaux

Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, Grenoble INP, LEPMI (France) –
roselyne.jeanne-brou@grenoble-inp.fr / renaud.bouchet@grenoble-inp.fr / didier.devaux@grenoble-inp.fr

## Introduction

* **Context:** Conventional Li-ion batteries can leak and react. [1]. Solution? Replace the liquid electrolyte by a non-flammable dry Solid Polymer Electrolyte (SPE).

➤ Ionic transport properties in SPEs have been largely studied in *through-plane* (L) configuration. Conversely, in *In-plane* (II) configuration studies are only dedicated to ionic conductivity (σ) of PEO homopolymer doped with a Li salt [2].

## Cell configurations

### Through-plane L

<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

### In-Plane //

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

### $\sigma_{\parallel}$ isotropy vs anisotropy

$$ \sigma_{\parallel} = \begin{pmatrix} \sigma_{\parallel} & 0 & 0 \\ 0 & \sigma_{\parallel} & 0 \\ 0 & 0 & \sigma_{\perp} \end{pmatrix} $$

<figure><img src="image_6.png" /></figure>

$$ \sigma_{\parallel, L} = \begin{pmatrix} \sigma_{\parallel} & 0 & 0 \\ 0 & \sigma_{\perp} & 0 \\ 0 & 0 & \sigma_{\parallel} \end{pmatrix} $$

<table><thead><tr><th>Temperature (°C)</th><th>Input (S.cm<sup>-1</sup>)</th><th>Output σ<sub>∥</sub></th></tr></thead><tbody><tr><td rowspan="3">80</td><td>σ<sub>∥</sub> = 1.02 10<sup>-3</sup></td><td rowspan="3">1.01 10<sup>-3</sup></td></tr><tr><td>σ<sub>∥</sub> = 1.02 10<sup>-3</sup></td></tr><tr><td>σ<sub>⊥</sub> = 5.67 10<sup>-4</sup></td></tr><tr><td rowspan="3">45</td><td>σ<sub>∥</sub> = 2.62 10<sup>-5</sup></td><td rowspan="3">2.60 10<sup>-5</sup></td></tr><tr><td>σ<sub>∥</sub> = 2.62 10<sup>-5</sup></td></tr><tr><td>σ<sub>⊥</sub> = 1.55 10<sup>-5</sup></td></tr></tbody></table>

### $\sigma_{\parallel}$ effect of geometry ($L_0/th$)

$$ \sigma_{x/\parallel} = \begin{pmatrix} \sigma_{\parallel} & 0 & 0 \\ 0 & \color{blue}\boldsymbol{x}\sigma_{\parallel} & 0 \\ 0 & 0 & \sigma_{\parallel} \end{pmatrix} \quad \text{with } \boldsymbol{x} = 1, 0.1 \text{ or } 10 $$

<figure><img src="image_7.png" /></figure>

* Current density localized at the edge of the electrodes

* Constant ionic current in the SPE cross section

➤ Cell constant: $k_{\parallel} = \frac{L}{w th}$

### $\Delta U(t), C, D_{amb}$

Nernst relation for a salt LiTFSI:

$$ \Delta U(t) = \frac{RT}{F} \ln \left( \frac{C^{+}}{C^{-}} \right) $$

2e Fick law:

$$ \frac{\partial C}{\partial t}(x, t) - D_{amb} \frac{\partial^2 C}{\partial x^2}(x, t) = 0 \\ \Rightarrow \ln(\Delta U) \propto \ln\left(\ln\left(\frac{C^{+}}{C^{-}}\right)\right) \propto D_{amb} $$

### $\sigma, t^+ + D^+ + D^-$

Nernst-Einstein equation:

$$ \sigma = \frac{F^2 (D^+ + D^-) \alpha C_{Li salt}}{RT} $$

With α, dissociation rate of the SPE
$C_{Li salt}$: concentration of the lithium salt

$$ \begin{cases} D^{-} = \frac{D_{amb}}{2t^{+}} \\ D^{+} = \frac{D_{amb}}{2(1 - t^{+})} \end{cases} $$

## References

[1] D. Lisbona, T. Snee, Process Saf. Environ., 89, 434 (2011).

[2] D. Golodnitsky and E. Peled, Electrochimica Acta, 45, 1431–1436 (2000)

[3] R. Bouchet et al. J. Electrochem. Soc., 150, A1385 (2003).

[4] M. Watanabe et al. Solid State Ion., 28-30, 911-917 (1988).

[5] S. D. Thompson and J. Newman, J. Electrochem. Soc., 136, 3362 (1989)

## Objectives

### Goal:

1. Understanding of the transport properties (conductivity $\sigma$, transference number $t^+$ and diffusion $D$) according to chains morphology, nanostructuration or ionic clusters.

2. Develop methodology to measure the transport properties in *through-plane* (II) vs. *in-plane* (L).

### Experiments: Measurements of various SPEs:

* Homopolymer of PEO/LiTFSI

* Copolymer based on PS-PEO-PS

* Single-ion SPE crosslinked-silica hybrid PEO Vinyl-TFSI (SI-CHSPE)

### Comsol modeling: Difference of potential (conductivity); relaxation of concentration gradients after a polarization step in II and L.

### Ionic conductivity $\sigma_{\parallel} \neq \sigma_{\perp}$: why?

The SPE electrolyte resistance $R_{el}$ is determined by Electrochemical Impedance Spectroscopy (EIS) [3]

$$ \sigma = \frac{k}{R_{el}} $$

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

<table><tr><td>M<sub>w</sub> (kg.mol<sup>-1</sup>)</td><td>PEO</td><td>PS-PEO-PS</td><td>Single-ion SPE:</td></tr><tr><td>EO/Li = 25</td><td>250-400k</td><td>6.7k-35k-6.7k</td><td>CHSPE</td></tr><tr><td>σ<sub>∥</sub> / σ<sub>⊥</sub> at 80°C</td><td>1.80 ± 0.05</td><td>0.91 ± 0.02</td><td>0.98 ± 0.02</td></tr></table>

≠ anisotropy according to the materials structure

## Polarization / Relaxation

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

$$ C^{+}(t) = C_{0} + \frac{\Delta C(t)}{2}; C^{-}(t) = C_{0} - \frac{\Delta C(t)}{2} $$

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

➤ In II, waiting the total polarization of the cell to measure only $D_{amb}$ // is not essential

<figure><img src="image_15.png" /></figure>

$$ t_0 = 0 \text{ s}; t_1 = 500 \text{ s}; t_2 = 10 \text{ 000 s}; t_3 = 100 \text{ 000 s} \\ t_4 = 200 \text{ 000 s}; t_5 = 400 \text{ 000 s}; t_{\infty} = 600 \text{ 000 s} $$

➤ Concentration gradients appear in all the SPE

➤ Linear domains appear at long relaxation time

## Transport properties - Conclusion

* In PEO and PS-PEO, anisotropy mainly due to the variation of $D^+$ and impact of transference number $t^+$

* The anisotropy experimentally measured may due to chain morphology along L and II

* In L for single-ion conductors, the passivation layers play a main role in the $t^+$ determination

<table><tr><td>M<sub>w</sub> (kg.mol<sup>-1</sup>)</td><td>PEO</td><td>PS-PEO-PS</td><td>Single-ion SPE:</td></tr><tr><td>EO/Li = 25</td><td>250-400k</td><td>6.7k-35k-6.7k</td><td>CHSPE</td></tr><tr><td>t<sup>+</sup> //</td><td>1.69 ± 0.02</td><td>1.23 ± 0.02</td><td>t<sup>+</sup> // = 1 ± 0.02</td></tr><tr><td>D<sup>-</sup> //</td><td>1.60 ± 0.01</td><td>0.88 ± 0.01</td><td>t<sup>+</sup> // = 0.89 ± 0.01</td></tr><tr><td>D<sup>+</sup> //</td><td>3.20 ± 0.01</td><td>1.08 ± 0.02</td><td>--</td></tr><tr><td>D<sup>+</sup> + D<sup>-</sup> //</td><td>1.80 ± 0.02</td><td>0.91 ± 0.02</td><td>--</td></tr></table>

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>