One problem with battery development is understanding how  performance changes with age. A good knowledge of this kind of degradation allows researchers to dismiss ineffective designs earlier and to concentrate on more promising ones. 

However, nobody has developed a good theoretical model of battery degradation so this kind of information has to be gathered from experiment, which can be a long and expensive task. For example, today’s lithium ion batteries degrade over thousands of cycles.

“The availability of a simple, but accurate, mathematical model of capacity fade and lifetime statistics could significantly accelerate battery development and commercialization,” say Matthew Pinson and Martin Bazant at the Massachusetts Institute of Technology in Cambridge.

And that’s exactly what these guys have developed–a simple model of the way battery capacity fades over time.

Batteries gradually degrade as the process of charging and recharging inevitably takes its toll. During this cycle, ions shuttle from one part of the battery to another, forcing themselves into lattices that are not always designed to accept them easily.

For example, when lithium ions enter a silicon lattice they cause it to expand in volume by a factor of four. That creates significant mechanical stresses during each charging cycle, which tend to tear the silicon apart. That’s why silicon, although otherwise promising, has yet to be used as an anode material. 

In lithium ion batteries, capacity fade occurs for a different reason. In this case, the electrolyte reacts with lithium at the negative electrode forming a permanent solid layer called the solid-electrolyte interphase. 

The battery continues to operate because lithium ions can travel through this layer with ease.

Nevertheless, this layer grows slowly. The reaction with the electrolyte removes lithium from the system, and after many thousands of cycles, this causes a gradual reduction in performance called capacity fade.  It is this that eventually stops the battery working. 

Pinson and Bazant’s new model simulates this process. They model the concentration gradients of lithium through the solid-electrolyte interphase and the concentration gradient of other reactive ingredients in the electrolyte. This allows them to simulate how the interphase layer evolves over time. 

“To our knowledge, this is the first attempt to theoretically predict the spatio-temporal distribution of solid-electrolyte interphase formation in a porous electrode,” say Pinson and Bazant. 

They go on to extend the model to work with other materials that rapidly degrade, such as silicon.

Of course, an important test of any model is how well it matches experimental observation. In this respect, the model works well, they say. “Our simple models are able to accurately fit a variety of published experimental data for graphite and silicon anodes.”   

That’s certainly promising but caution is always advisable in the notoriously complex world of electrochemistry. If a simple model can help to explain complex behaviour, all well and good. But there will be plenty of doubters who will need convincing.

The real test will be whether this model has predictive value in real battery research–is it reliable enough to help determine the direction of future work? 

That’s still an open question.

Ref: arxiv.org/abs/1210.3672: Theory of SEI Formation in Rechargeable Batteries: Capacity Fade, Accelerated Aging and Lifetime Prediction