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Digital archive of theses discussed at the University of Pisa


Thesis etd-02142023-172458

Thesis type
Tesi di dottorato di ricerca
Thesis title
Mathematical modelling of thermo-electrochemical phenomena in lithium-based batteries
Academic discipline
Course of study
tutor Prof. Bertei, Antonio
relatore Prof. Nicolella, Cristiano
controrelatore Prof. Mauri, Roberto
  • fast charge
  • Li-O2 battery cathode design optimisation
  • lithium plating
  • lithium-ion battery modelling
  • lithium-oxygen battery modelling
  • P2D model
  • redox mediated Li-O2 battery charge modelling
  • redox mediated Li-O2 battery discharge modelling
  • thermo-electrochemical model parametrisation
Graduation session start date
Release date
There is a clear and urgent need for rechargeable batteries of higher power/energy density, reduced charging time and environmental footprint. Nowadays, Li-ion batteries based on graphite/metal-oxide chemistries are the state-of-the-art. However, their performance during high-rate discharge and charge operations is currently limited by the internal physical phenomena of (de)intercalation occurring at the electrodes. In particular, the negative electrode results as the most critical component due to the phase separation phenomenon peculiar to graphite electrodes, which hinders high-rate processes and is strongly coupled to the onset and increase of degradation phenomena. Additionally, the rise in inner temperature and heat generation become critical upon harsh external conditions or high-rate operations, and they may lead to unsafe conditions and thermal stresses, increasing the degradation phenomena or even escalating to thermal runaway. On the cathode side, lithium transition-metal oxides play a crucial role in storing charge in cathodes of Li-ion batteries. However, their high toxicity and low natural abundance result in high costs and environmental issues.

To overcome the energy/power limitations and environmental issues of Li-ion batteries, Li-air batteries emerged as suitable candidates showing rechargeability, high volumetric and gravimetric energy densities, and minimal environmental impact. These characteristics can be achieved thanks to their internal structure, which should comprise lithium-metal anodes and carbon cathodes, using oxygen as a reactant. Among various cell configurations, aprotic lithium-air batteries result as the most performing and reliable structure so far, being characterised by an organic electrolyte, enabling the highest deposition of the lithium peroxide (Li2O2), which is the main product of the discharge process. Indeed, Li-air batteries seem promising, but their performances are currently limited by the interplay between the cathode's microstructure and the lithium-peroxide deposition. Upon discharge, Li2O2 is deposited on the carbon surface resulting in an insulating layer which hinders the discharge process, resulting in low capacity and poor volumetric efficiency. Recently, the introduction of redox mediators improved the performance of these cells by enabling the delocalisation of the Li2O2 deposition inside the bulk of cathode porosity. However, Li2O2 deposition, oxygen transport and microstructure evolution during discharge/charge remain limiting phenomena that must be unravelled to increase the performance of these batteries.

It is clear that both Li-ion and Li-air batteries share common limiting features that can be summarised in the evolution and understanding of phenomena occurring at physical interfaces over time during operation. For this reason, the development of physics-based models able to accurately simulate the evolution of such interfaces over time in different operative conditions represents a game-changing tool that can be used to boost significantly research activities.

Therefore, this thesis presents a framework for microstructural-electrochemical modelling of Li-ion and Li-air batteries. The models incorporate the microstructure and particle information of battery components to account for electrochemical discharge/charge reactions. Microstructural properties are inputs for physics-based electrochemical models, using mass and charge balances in a macro-homogeneous approach to describe transport and reactions at the mesoscale. This foundation supports advanced models developed in this work to understand and overcome limitations in Li-ion and Li-air batteries.

The first part of the thesis deals with Li-ion battery modelling. The well-shared Pseudo-2-Dimensional (P2D) model based on the Porous Electrode Theory (PED) is used as the model foundation. The P2D model is extended with the introduction of the energy conservation equation and the mathematical framework used to model the heat generation in the components within the battery based on literature research. Simultaneously, the results of extensive literature search on the P2D model parameters are presented with a particular focus on the thermal parameters and how their uncertainty may affect the temperature and the performance predictions. Two approaches to modelling the transport of charge in the electrolyte are critically compared and discussed; these approaches are the Concentrated Solution Theory (CST), currently the most shared approach, and the generalised Nernst-Planck (gNP) framework. In particular, the thermodynamic description of the electrolyte between the two approaches is critically analysed, and the repercussion on simulation results are investigated both in terms of performance indicators, such as voltage, accessible/restored capacity, and max temperature, as well as for the onset of degradation phenomena. The thermo-electrochemical P2D model is then integrated with advanced physics to model the (de)intercalation process in graphite anodes. A phase field modelling approach is used within a P2D model to simulate the staging phenomenon of graphite and validated against world-class experimental data. Furthermore, degradation phenomena kinetics for the lithium plating and the Solid-Electrolyte-Interface (SEI) evolution are implemented. Such integration of kinetics leads to a comprehensive understanding of the interplay between (de)lithiation, staging, and degradation processes in Li-ion batteries. This forms the foundation for future-generation charging protocols.

The second part of the thesis concerns Li-air battery modelling. A multi-length scale microstructural-electrochemical model is presented for the first time, enabling the modelling of discharge and charge operations of Li-air batteries, including redox mediators pathways. A 1D macro-homogeneous approach is used to simulate the evolution of the cathode microstructure during the discharge process accounting for the redox-mediated solution-growth mechanism of Li2O2, which affects both the available porosity and the nucleation interface for further deposition of Li2O2. After a thorough analysis of experimental evidence, the model framework is improved with a more accurate description of the microscopic behaviour of the cathode microstructure. The latter phenomenologically considers agglomeration and pore-clogging effects, which are critical aspects of the discharge process affecting the mass transport in the electrolyte phase. The 1D model is then extended to a 2D model and simultaneously validated against experimental data obtained through novel techniques able to provide macroscopic indicators, such as voltage and accessible capacity and Li2O2 distribution within the cathode thickness, in various operative conditions. Finally, the validated 2D model is used to perform an optimisation study targeted to the definition of micro-embedded channels used to prevent an early discharge interruption due to oxygen depletion in the cathode thickness at high discharge rates. The above mathematical framework is then applied to a charging scenario where the microstructure-electrochemical model is used to screen the impact on charging performance of a variety of redox mediators with different equilibrium, kinetic, and transport characteristics. The sensitivity of the simulation results of voltage, capacity, and Li2O2 distribution to different redox mediator properties is investigated, and the critical phenomena currently limiting the charging process are unravelled.

The application of these integrated models confirms a strong coupling between electrode microstructure, the evolution of phases, and cell thermo-electrochemical behaviour characteristic of Li-ion and Li-air batteries. Only by considering this interaction can a model provide quantitative information and sound predictions to overcome the current technology limitations.

In conclusion, this thesis presents physics-based models that overcome the current state-of-the-art. These models, which incorporate the mechanistic understanding of key processes in Li-based batteries, allow for a thorough analysis and understanding of critical phase evolution over time. This leads to valuable insights into the interplay of the underlying physics. As a result, these models serve as a reliable predictive tool that can simulate the behaviour of Li-based batteries with high accuracy, based on measurable parameters, and assist in addressing current challenges in Li-based battery research.