Inverse Modelling Approach to the Determination of Concentration-Dependent Transport Properties in Electrolytes: The Effect of Ion Pairing
Notice bibliographique
Résumé
The goal of the present investigation was to extend the recently proposed inverse modelling approach for determining concentration-dependent transport properties (salt diffusivity and Li + cation transference number) to concentrated lithium salt solutions in solvents with relatively low permittivity. We demonstrated in our previous studies that NMR concentration profiles can be used for estimating the concentration dependent transport properties of LiTFSI solution in propylene carbonate (PC) under minimal assumption, including that of negligible ion pairing (simplified transport model) [1], which is valid for solvents with relative high permittivity [2] (ε r ≈ 65 for PC). Herein we consider the case where ion paring effects cannot be neglected, due to the low permittivity of the solvent, as is the case for concentrated solutions of Li salts in mixed organic carbonate solvents (ε r ≈ 26 for EC:DMC 1:1). The data for the present study was obtained in the form of NMR intensity images of the 19 F nuclei in the PF 6 - anions of LiPF 6 dissolved in a binary mixture of ethylene carbonate (EC) and dimethyl carbonate (DMC), recorded under galvanostatic conditions. The NMR images were then post-processed to obtain lithium concentration profiles. The formation of non-negligible amounts of ion pairs in the present work significantly affects the estimation of transport properties of the system. As a result, the simplified transport model produces thermodynamically inconsistent results, manifested as negative transference numbers obtained from the inverse modelling analysis (Fig. 1). To remedy this situation, we considered an extended transport model which assumes that oppositely charged ions combine to form neutral ion pairs and which tracks the concentration of neutral ion pairs in addition to the concentration of free ions. However, due to the presence of a reaction term describing the formation and disintegration of ion pairs, the resulting PDE system is extremely stiff. Using methods of asymptotic analysis, corresponding to the limit of fast reaction rates, we have reduced the modeling problem to a more simple system describing the evolution of the total lithium concentration, which is computationally tractable. As this reduced system may not satisfy all boundary conditions of the original extended system, an additional material property called boundary transference number was introduced and its optimal dependence on the total concentration was identified via inverse analysis. The unknown material properties are concentration dependent (except for the equilibrium constant K ) and are reconstructed with minimal assumptions using methods of variational optimization, to minimize the least-square error between the experimentally determined and simulated concentration values. The optimization problem is solved using a gradient-based method with a careful treatment of uncertainties resulting from the presence of noise in the experimental data. A key element of our computational approach is identification of the sensitivity of the PDE system solutions to perturbations of the constitutive relations, which is achieved through a novel adjoint-based approach. As shown in Fig. 2, the reconstruction produces thermodynamically consistent results for the Li + transference number under conditions when ion pairing effects cannot be neglected. References: A.K. Sethurajan, S.A. Krachkovskiy, I. C. Halalay, G.R. Goward, B. Protas, J. Phys. Chem. B, 119 , 12238 (2015). Y. Marcus and G. Hefter, Chem. Rev., 106 , 4585 (2006). Figure 1. The simplified diffusion-migration model equations and inverse modelling results for LiPF 6 /EC:DMC 1:1 v/v. The assumption of negligible ion pairing yields nonphysical values for the Li + transference number. Note also that the cost functional is above the 95% confidence bound. ( D = salt diffusion coefficient, t + = cation transference number; units for the ion concentration c are mM). Figure 2. Extended diffusion-migration model (including ion pairing) equations and results of the inverse modeling analysis for LiPF 6 /EC:DMC 1:1 v/v. ( D i = salt diffusion coefficient for free ions, D 0 = salt diffusion coefficient for ion pairs, t + = cation transference number, r + = boundary transference number for cations, c t = c i + c 0 ; units for the salt concentration c t are mM). Figure 1
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Prédiction distillée sur la base complète
Imitation des enseignantsNi prévalence calibrée, ni vérité terrain. Validation humaine à venir. Apprise à partir de 10 348 étiquettes directes de Codex et de 10 348 étiquettes directes de Gemma. Le mode candidate est l'union des têtes enseignantes seuillées; le consensus est leur intersection. Ces sorties portent le statut machine_predicted_unvalidated et ne sont ni des étiquettes humaines ni des étiquettes directes de modèles de pointe.
Scores Codex et Gemma par catégorie
| Catégorie | Codex | Gemma |
|---|---|---|
| Métarecherche | 0,000 | 0,000 |
| Méta-épidémiologie (sens strict) | 0,000 | 0,000 |
| Méta-épidémiologie (sens large) | 0,000 | 0,000 |
| Bibliométrie | 0,000 | 0,000 |
| Études des sciences et des technologies | 0,000 | 0,000 |
| Communication savante | 0,000 | 0,000 |
| Science ouverte | 0,000 | 0,000 |
| Intégrité de la recherche | 0,000 | 0,000 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,000 | 0,000 |
Scores machine (provisoires)
Les deux têtes enseignantes du modèle étudiant, lues sur ce travail. Un score ordonne la base pour la relecture; il n'affirme jamais une catégorie, et le statut de validation accompagne chaque rangée tel quel.
Scores de référence d'un modèle non mature (critères de maturité non atteints, 7 itérations). Un score ordonne; il n'affirme jamais une catégorie.
score_only:v0-immature-baseline · tel quel depuis la passe de notation : score_only signifie que le nombre peut ordonner les travaux, et qu'aucune étiquette de catégorie n'en découleClassification
machine, non validéePrédiction automatique; un appel candidat d’une seule tête enseignante, pas un consensus.
Le détail, modèle par modèle et score par score, se trouve en fin de page sous « Comment cette classification a été obtenue ».