(Invited) Bridging Long Temporal Scales: Durability Analysis of Electrochemical Systems
Authors: Fuller Thomas F 
Published: February 2020

Fundamental understanding of the mechanisms of degradation of electrochemical systems for energy storage and conversion is receiving intense investigation. A vast number of energy storage and conversion devices that share common features, i.e., a reliance on nano-scaled materials that are not thermodynamically stable, and whose costs are too high compared to existing technologies. Models have been developed with detailed physics for many degradation phenomena, for example, formation of the solid electrolyte interphase in lithium-ion batteries, dissolution and ripening of precious metal catalyst in proton exchange membrane fuel cells, and corrosion of catalyst supports. Increasingly these models deal with ever smaller time and length scales.
At the same time, to allow for rapid advances in these electrochemical technologies, we must not only understand the degradation phenomena but also have some predictive capability that a physical model provides. Design procedures used for batteries for satellite applications illustrate this point. The aerospace industry requires that cells be tested for 70 % of life to become qualified for space. Therefore, a satellite battery for a 10-year mission would require a full 7 years of testing in the lab using the final design. As a result, these applications cannot take advantage of the latest technology. Similarly, fuel cells and energy storage devices for automobiles require useable lifetimes of more than 10 years. The development of thorough fundamental understanding of the mechanisms of failure combined with physics-based models is essential.
The timescale for these detailed physical models are much shorter than the timescale for analysis of lifetime (years) behavior. Therefore, a computationally efficient means of bridging across these time scales is needed. Here our purpose was to develop the framework for analysis of systems that combine detailed performance and degradation. This framework has the potential to transform the way that these systems are designed and operated.
The computational expense of these meticulous degradation models does not permit their practical use in higher-level systems analysis. It is important to include detailed physics, but computationally expensive. One answer is to use response surface methodology. Indeed, we have used this to incorporate electrochemical degradation into a hybrid-system design for a vehicle. Briefly this approach runs the detailed simulation many times to map the anticipated design space. Then surrogate models are developed to represent the output of the detailed model. One obstacle with this method is that each time the detailed model is modified with new physics or even just a parameter change, the process must be repeated from the beginning. An alternative approach is developed that follows the methodology of Kevrekidis et al. The detailed model is run with small time increments for a short period of time, long enough so the time derivative can be evaluated accurately. Then using a forward Euler scheme, for example, a large step in time is taken. The temporal variations of the dependent variables are well-behaved, as illustrated with particle size. The metric for success is straightforward—savings in computational time over running the full detailed model. These steps can be adjusted, much like adaptive time stepping, as needed to achieve the desired accuracy. In addition to the computational efficiency, the advantage over RSM is that if the underlying detailed model is changed, no changes are needed in the framework.
This methodology is applied to the dissolution of platinum in proton exchange fuel cells investigated for long-term automotive application. gPROMS is used to solve the differential equations and provides a framework to bridge the disparate time scales.