Engineers rely on computational tools to develop new energy storage technologies, which are critical for capitalizing on sustainable energy sources and powering electric vehicles and other devices. Researchers have now developed a new classical physics model that captures one of the most complex aspects of energy storage research - the dynamic nonequilibrium processes that throw chemical, mechanical and physical aspects of energy storage materials out of balance when they are charging or discharging energy.
The new Chen-Huang Nonequilibrium Phasex Transformation (NExT) Model was developed by Hongjiang Chen, a former Ph.D. student at NC State, in conjunction with his advisor, Hsiao-Ying Shadow Huang, who is an associate professor of mechanical and aerospace engineering at the university. A paper on the work, "Energy Change Pathways in Electrodes during Nonequilibrium Processes," is published in The Journal of Physical Chemistry C.
But what are "nonequilibrium processes"? Why are they important? And why would you want to translate those processes into mathematical formulae? We talked with Huang to learn more.
The Abstract: This is a highly technical paper, so I want to break it down piece by piece. To start with, what are "nonequilibrium processes"? Why are they important?
Hsiao-Ying Shadow Huang: When a lithium-ion battery is disconnected and sits for hours, it approaches equilibrium. In an equilibrium state, lithium-ion batteries exhibit no current flow, have uniformly distributed lithium-ion concentrations in the electrolyte and electrode materials, maintain stable temperatures without gradients (meaning the temperature is the same throughout the material), and present stable electrode potentials with no net chemical reactions occurring.
Even during slow charging and discharging, a lithium-ion battery is operating under nonequilibrium conditions.
Charging and discharging of lithium-ion batteries is fundamentally a nonequilibrium process, involving multiple transport phenomena that deviate significantly from thermodynamic equilibrium. That is, it pushes it far from its natural resting state, causing several physical and chemical changes inside the battery that can impact its performance and lifespan. Even during slow charging and discharging, the battery is operating under nonequilibrium conditions. But during rapid charging and discharging, the deviation from equilibrium is more pronounced.
Rapidly charging or drawing energy from a lithium-ion battery requires lithium ions to move rapidly through the electrolyte of the battery and into the electrodes. This creates an uneven distribution of ions with some areas becoming crowded with ions while others are depleted. This mass transport imbalance drives intense movement that deviates significantly from the lithium-ion battery's usual stable state, as the system cannot maintain uniform concentrations throughout.
But there are also other factors that come into play under nonequilibrium conditions.
Fast operation generates substantial heat, which spreads unevenly throughout the battery, creating hot and cool spots. These temperature differences cause chemical reactions to proceed at different rates in different locations, making the entire system increasingly unstable and further removed from its equilibrium state.
Under rapid charge and discharge conditions, the battery operates at voltages far removed from its ideal open-circuit voltage, meaning it cannot function in a balanced or energy-efficient manner. This electrochemical imbalance requires large overpotentials to drive the high current flows, again pushing the system further from equilibrium.
And the rapid movement of lithium-ions in and out of battery materials causes physical expansion and contraction that occurs faster than the materials can mechanically adjust, creating significant internal stress. This mechanical strain can lead to the formation of tiny cracks in the electrode materials and cause accelerated wear in certain parts of the battery. In materials like LiFePO4, these conditions force internal structural changes to occur under kinetically rushed conditions rather than through the naturally stable thermodynamic processes that would occur during slow operation.
In short, nonequilibrium processes can pose significant challenges when it comes to both having the battery operate efficiently and protecting the structural integrity of the battery.
TA: Why is it important to understand these nonequilibrium processes?
Huang: Understanding these nonequilibrium aspects is crucial for the following reasons:
- You must understand nonequilibrium processes to develop protocols for fast charging and discharging of energy from lithium-ion batteries that balance speed with safety and help to extend the longevity of lithium-ion batteries. (The challenge in rapid charging and discharging is managing nonequilibrium processes to achieve fast energy storage while minimizing degradation mechanisms that also arise from operating far from equilibrium.)
- Nonequilibrium processes are critical for developing thermal management systems to handle the heat generated by these processes.
- Understanding these processes is critical when designing materials that can be used in electrodes to better handle nonequilibrium transport.
TA: There are not established classical physical models - mathematical formulas - that adequately capture those nonequilibrium processes? Is that correct?
Huang: There are classical physical models for lithium-ion batteries. However, their predictive accuracy is often limited. This limitation arises primarily from: (i) the use of model inputs with constrained accuracy, often based on linear assumptions; (ii) the omission of complex system phenomena, such as mass transport; and (iii) an incomplete understanding of the underlying processes and characteristics of lithium-ion battery systems - for example, widely used commercial simulation software is typically restricted to modeling equilibrium processes.
TA: Why are these models important?
Huang: Accurate classical physical models provide the essential mathematical foundations and conceptual frameworks that support computational modeling of materials and enable machine learning (ML) programs to address questions related to materials science and engineering. The differential equations, optimization theory and statistical methods developed in physics directly translate into core ML algorithms - from gradient descent techniques to neural network operations. Most importantly, physics demonstrates how complex phenomena can be understood through mathematical abstraction and iterative refinement, the same approach used in training ML models. Without the mathematical rigor, analytical thinking, and modeling paradigms from classical physics, machine learning would lack the computational tools and intellectual framework necessary to extract meaningful patterns from data and make reliable predictions.
TA: So, what did you do here?
Huang: In this study, we propose a new mechanism to explain how lithium-ion battery materials like LiFePO4 (LFP) and lithium nickel manganese cobalt oxides (NMC) undergo phase transitions under nonequilibrium conditions - such as fast charging or discharging. We introduce the concept of path factors, which influence how energy changes within the material during lithium-ion insertion and removal. These factors interact with key properties like lithium content, mechanical strain, structural defects (dislocations) and material order. Our simulations show that dislocation density, which increases with faster electrochemical reactions, plays a critical role in driving structural changes. By modeling these effects across multiple material states - like lithium-rich vs. lithium-poor and ordered vs. disordered - we capture how the internal structure shifts dynamically.
We validated our model by comparing simulation results to experimental data for both LFP and NMC materials across various charge/discharge rates. The agreement supports our pathway-altering mechanism as a powerful tool to understand and potentially improve battery performance under nonequilibrium conditions.
In other words, our model can be incorporated into computational tools to improve our ability to engineer better batteries.
TA: Can the NExT Model you developed be used to address a variety of nonequilibrium processes? And, if so, why did you focus specifically on electrodes and lithium-ion batteries in the journal article?
Huang: Extensive experimental data are essential for developing accurate classical physical models, as they provide the empirical basis needed to transform theoretical ideas into reliable scientific understanding. For lithium-ion battery materials such as LFP and NMC, a wealth of experimental results from various research groups has become available. This abundance of data was a key motivation for developing the NExT Model, which is specifically designed to capture the behavior of these widely studied systems. By drawing on experimental findings across different conditions, length scales and phenomena, we ensure that our mathematical formulations reflect real physical processes rather than remaining abstract theoretical constructs. The iterative interplay between modeling and experimentation enables us to identify model limitations, adjust key parameters, and uncover new physical insights - ultimately leading to more precise and comprehensive representations of complex systems.
TA: What are other applications that can make use of the NExT Model?
Huang: Although our current published work focuses on lithium-ion battery materials such as LFP and NMC, the underlying pathway-altering mechanism and the concept of path factors are broadly applicable and can be extended to other energy storage systems, including multivalent battery materials (e.g., those based on magnesium, calcium or zinc). These systems often exhibit more complex ion-host interactions and phase behaviors, where nonequilibrium effects play an even more critical role. By capturing the coupled evolution of dislocation dynamics, mechanical strain, and multi-state phase transitions, our framework (i.e., the NExT Model) contributes to the advancement of computational materials science, offering a predictive and mechanistic tool for investigating complex, rate-dependent processes. In the broader context, this approach supports the rational design of next-generation energy storage materials and devices, accelerating materials discovery and optimization through physics-informed modeling grounded in experimental validation.
