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Impact of unsolvated lithium salt concentration on the ions transport pathway in polymer electrolyte (LiTFSI-PEO): empirical mathematical model to predict the ionic conductivity

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Abstract

The effect of the lithium salt LiTFSI molality into the PEO-based electrolyte on the ionic conductivity was investigated in this work. To begin, the experimental evolution of LiTFSI-PEO electrolyte's ionic conductivity as a function of molality was analyzed, and hypotheses were put out to explain how ionic transport occurs in a heterogeneous microstructure of polymer electrolytes. To forecast the ionic conductivity in the electrolyte LiTFSI-PEO as a function of molality, an empirical mathematical model was then proposed, taking the phenomena predicted to occur into account. The proposed theoretical model presupposes that lithium salt's solvation state (total or partial solvation) and the steric effect brought on by heterogeneous areas are related to the conduction of ions (at the microscopic scale). The model is adjusted to accurately depict the entire experimental curve, which is thought to have three distinct domains. In the first domain, where the molality m is less than 1 mol/kg, the oxygen atoms completely solvate the lithium salt. The conduction is believed to be favorable in this situation since the released solvated lithium ions linearly fluctuate against the molality. The partial solvation of lithium corresponds to the second domain (1 mol/kg ≾ m ≾ 2 mol/kg), where the conductivity of the polymer electrolyte slightly increases with increasing molality. In the third domain, where m is greater than 2 mol/kg, the loss in ionic conductivity is caused by steric effects, as some of the lithium salt (LiTFSI) does not ionize and becomes immobilized, obstructing the transport pathway. Finally, the model was expanded to include how temperature affects ionic conductivity. The prediction model was effectively validated when it was put up against the findings of experiments conducted by various authors.

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Abbreviations

\(\mathrm{c}=\frac{{\mathrm{c}}_{+}}{{\upnu }_{+}}=\frac{{\mathrm{c}}_{-}}{{\upnu }_{-}}\) :

Normalized molarity of binary salt, [\(\mathrm{mol}\ {\mathrm{m}}^{-3}\)]

\({\mathrm{c}}_{0}\) :

Polymer molarity, [\(\mathrm{mol}\ {\mathrm{m}}^{-3}\)]

\(\mathrm{D}\) :

Solute diffusion coefficient, [\({\mathrm{m}}^{2}/\mathrm{s}\)]

\(\mathcal{D}\) :

Thermodynamic diffusion coefficient of solute, [\({\mathrm{m}}^{2}/\mathrm{s}\)]

\({\mathcal{D}}_{\pm }\) :

Pairwise diffusion coefficient of cations with respect to anions, [\({\mathrm{m}}^{2}/\mathrm{s}\)]

\({\mathcal{D}}_{0-}\) :

Pairwise diffusion coefficient of anions with respect to polymeric solvent, [\({\mathrm{m}}^{2}/\mathrm{s}\)]

\(\mathrm{F}\) :

Faraday constant, [96 486 C/mol]

\({\mathrm{f}}_{\pm }\) :

Mean molar activity coefficient \({\left({\mathrm{f}}_{+} {\mathrm{f}}_{-}\right)}^{0.5}\)

\({\mathrm{f}}_{+}\) :

Molar activity coefficients of cations

\({\mathrm{f}}_{-}\) :

Molar activity coefficients of anions

\(\mathbf{i}\) :

Density of ionic current, [\(\mathrm{A}\ {\mathrm{m}}^{-2}\)]

\(\mathbf{m}\) :

Molality of the lithium salt, [\(\mathrm{mol}\ {\mathrm{kg}}^{-1}\)]

\({\mathbf{m}}^{*}\) :

Starting partial dissolution molality, [\(\mathrm{mol}\ {\mathrm{kg}}^{-1}\)]

\({\mathbf{m}}_{\mathrm{lim}}\) :

Critical molality marking the starting \(\upepsilon\) point of the decrease of the ionic conductivity, [\(\mathrm{mol}\ {\mathrm{kg}}^{-1}\)]

\({\mathrm{m}}_{\mathrm{PEO}}\) :

Mass of PEO, [\(\mathrm{kg}\)]

\({\mathrm{m}}_{\mathrm{salt}}\) :

Mass of lithium salt, [\(\mathrm{kg}\)]

\({\mathrm{M}}_{\mathrm{salt}}\) :

Molar mass of the salt, [\(\mathrm{g}\ {\mathrm{mol}}^{-1}\)]

\({\mathrm{M}}_{\mathrm{EO}}\) :

Molar mass of the monomer ethylene oxide (EO), [\(\mathrm{g}\ {\mathrm{mol}}^{-1}\)]

\({\mathrm{M}}_{\mathrm{PEO}}\) or \({\mathrm{M}}_{\mathrm{w}}\) :

Molar mass of the polymer ethylene oxide (PEO), [\(\mathrm{g}\ {\mathrm{mol}}^{-1}\)]

\({\mathrm{n}}_{\mathrm{PEO}}\) :

Moles number of the PEO, [\(\mathrm{mol}\)]

\({\mathrm{n}}_{\mathrm{salt}}\) :

Moles number of the lithium salt, [\(\mathrm{mol}\)]

\(\mathrm{t}\) :

Time, [\(\mathrm{s}\)]

\({\mathrm{t}}_{+}^{0}\) :

Transference number of the cation

\(\left(1+\frac{\partial {\mathrm{lnf}}_{\pm }}{\partial \mathrm{lnc}}\right)\) :

Thermodynamic factor

\({\mathbf{v}}_{0}\) :

Solvent velocity (here the polymer PEO i.e., polyethylene oxide), [\(\mathrm{m}\ {\mathrm{s}}^{-1}\)]

\({\mathrm{V}}_{\mathrm{el}}\) :

Total volume of the electrolyte, [\(\mathrm{L}\)]

\({\mathrm{V}}_{\mathrm{PEO}}\) :

Total volume occupied by PEO fibers, [\(\mathrm{L}\)]

\({\mathrm{V}}_{\mathrm{salt}}\) :

Total volume occupied by the lithium salt, [\(\mathrm{L}\)]

\({\overline{\mathrm{V}} }_{\mathrm{salt}}\) :

Partial molar volume of lithium salt, [\({\mathrm{m}}^{3}/\mathrm{mol}\)]

\({\overline{\mathrm{V}} }_{\mathrm{PEO}}\) :

Partial molar volume of the PEO, [\({\mathrm{m}}^{3}/\mathrm{mol}\)]

R:

Universal gas constant, [\(\mathrm{J}\ {\mathrm{mol}}^{-1}\, {\mathrm{K}}^{-1}\)]

\(\mathrm{T}\) :

Temperature of the polarized electrochemical cell, [\(\mathrm{K}\)]

\({\mathrm{T}}_{\mathrm{r}}\) :

Reference temperature at which model coefficients were deduced, \(\mathrm{K}\)

\(\upepsilon\) :

Ratio of hard volume by electrolyte volume

\(\upkappa\) :

Ionic conductivity, [\(\mathrm{S}{\, \mathrm{m}}^{-1}]\)

\({\upkappa }_{\mathrm{eff}}\) :

Effective ionic conductivity, [\(\mathrm{S}{\, \mathrm{m}}^{-1}]\)

\({\upkappa }_{\mathrm{Newman}}\) :

Ionic conductivity versus Newman theory, [\(\mathrm{S}{\, \mathrm{m}}^{-1}]\)

\({\upkappa }_{\mathrm{model}}\) :

Ionic conductivity versus our model \({\upkappa }_{\mathrm{eff}}\), [\(\mathrm{S}{\, \mathrm{m}}^{-1}]\)

\({\upnu }_{+}\) :

Stoichiometric coefficient of cations of the lithium salt

\({\upnu }_{-}\) :

Stoichiometric coefficient of anions j of the lithium salt

\(\upnu\) :

Number of moles of salt per unit of mole of electrolyte \({\upnu }_{+}+{\upnu }_{-}\)

ρ:

Density of the electrolyte, [\(\mathrm{kg}\ {\mathrm{m}}^{-3}\)]

\(\Phi\) :

Electric potential, [\(\mathrm{V}\)]

\({\mathrm{\chi}}\) :

Fraction of solvated lithium ions

\(\mathrm{Eff}\) :

Effective

\(\mathrm{Exp}\) :

Experimental

\(\mathrm{Newman}\) :

Based on Newman model

\(\mathrm{Model}\) :

Modelling

\(\mathrm{Salt}\) :

Lithium salt LiTFSI

\(\mathrm{PEO}\) :

Poly (ethylene oxide) PEO

\(+\) :

Cations

\(-\) :

Anions

\(0\) :

Polymeric solvent (PEO)

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Acknowledgements

This work was financially supported by to ANRT « Association Nationale de la Recherche et de la Technologie » and RENAULT SA (Renault Technocentre, 78084 Guyancourt, France).

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Authors and Affiliations

  1. Laboratoire de Génie Chimique, UMR CNRS 5503, Université Toulouse III - Paul Sabatier, 118, route de Narbonne, 31062, Toulouse Cedex 9, France

    Sanatou Toe, Fabien Chauvet, Jean-Christophe Remigy & Theo Tzedakis

  2. Renault Technocentre, 78084, Guyancourt, France

    Sanatou Toe & Lucie Leveau

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ST: Conceptualization, Software, Data curation, Formal analysis, Investigation, Methodology, Validation, Visualization, Writing - original draft preparation. FC: Conceptualization, Formal analysis, Investigation, Validation, Writing - review & editing. LL: Conceptualization, Formal analysis, Investigation, Validation, Writing- review & editing. J-CR: Conceptualization, Formal analysis, Investigation, Validation, Methodology, Writing - review & editing. TT: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Writing – review & editing.

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Toe, S., Chauvet, F., Leveau, L. et al. Impact of unsolvated lithium salt concentration on the ions transport pathway in polymer electrolyte (LiTFSI-PEO): empirical mathematical model to predict the ionic conductivity. J Appl Electrochem 53, 1939–1951 (2023). https://doi.org/10.1007/s10800-023-01900-4

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