Hierarchical characterization of batteries

Electrochemistry is fundamentally an interfacial science, dealing with reactions that happen at the interface between an electron conductor and an ion conductor. In many cases, including most practical batteries, this is a solid-liquid interface. Most batteries are consequently designed to be composed largely of interface. Often compressed particles of active material make up the electrodes and liquid electrolyte fills the pore space between the particles. The goal of battery engineering revolves around questions of either energy or power, and what value of these can be achieved in a device of a given mass, volume, or cost. Thus some metrics of battery success dealing with energy are: specific energy (Wh/kg), energy density (Wh/L), or capital cost ($/kWh). High specific energy is crucial for automotive batteries, while low capital cost is most important for large, stationary batteries at the building or grid scale.

Hierarchy of battery development

Another fundamental feature of electrochemistry is that it by necessity involves the interplay of two electrodes, an anode and a cathode. Experimental techniques exist to test electrodes in isolation, but in practical devices such as batteries the electrodes usually interact. Device performance is determined not only by the performance potential of each electrode, but also by the effect of each electrode on the other. Because of this and the need to maximize interface, battery design is hierarchical (see fig. above): (i) active materials are chosen due to their voltages and rate capabilities; (ii) the active materials are formed into useful electrodes, which may have high surface area; (iii) the two electrodes are integrated into a device; and (iv) devices are connected (in series or parallel) to form a system, if needed.

This hierarchy requires specialized characterization at every level. There has long been an established toolkit for electrochemical materials characterization, but true device-level characterization is only now coming into its own as techniques are developed to collect microscopic data from within sealed batteries. Device-level knowledge beyond voltage/current (E/I) data is extremely powerful and promises to advance understanding into the complex mechanisms that occur inside cycling batteries. An overreliance on materials-level characterization ignores conditions arising from device-level aspects. One example is electrolyte concentration at the outer radius of a AA battery, which falls from its initial value during discharge, and is thus different than the same concentration in a D battery, which rises due to a much longer transport path to the anode. With materials-level characterization there is also the danger for a fallacy of composition, in which remarkable capabilities of the materials are inferred to the device without justification, based on a misunderstanding of battery design principles.

Dendrites: Zinc and Lithium

I just got back from the spring Electrochemical Society conference in Chicago, where I was presenting in a session on Dendritic Growth and Interface Stability. Several people showed in operando images of dendrites growing in real time. One in particular I liked a lot was by Layla Mehdi at PNNL … she has a specialized test cell to observe lithium dendrites by transmission electron microscopy. I’ve done a lot of work on dendrites, and what I care most about is why dendrites form. While I was watching all these great movies of dendrites growing, I wondered something I often wonder: why do some dendrites look like they grow from the tip, and some from the bottom?

Dendrites can be the result of multiple mechanisms. They’re often a mass transport effect, but sometimes not. If you flow electrolyte over dendrites, you can directly observe the kinetic growth limit at their tips (plug for my paper about about that), but the non-growing locations aren’t really mass-transport starved … rather, they are in locations of low overpotential. So, that all makes sense, but still sometimes I’m baffled. Consider the two movies below …

The first one (this is my data from the paper above btw) shows zinc dendrites growing in a 1 mm wide flow channel, with alkaline electrolyte flowing from top to bottom. Essentially this is a model of a zinc flow battery. Growth here is potentiostatic (2.5 V) with oxygen generation at the electrode on the right. The important thing is watch the tips. That’s where the growth is. The bases of the dendrites are static.

Here is an analogous movie of a lithium dendrite growing in a flow channel. This was taken by Owen Crowther (paper here), who’s now working at Eagle Picher. If you focus on the dendrite tip, it doesn’t look like there’s any action there. Growth seems to come from the base (or middle). But that would be the location of lowest overpotential and lowest mass transport, so there must be something catalytic happening. Perhaps it’s because of a locally thin SEI layer.

Dimensional analysis of batteries

Now that high performance batteries are a big part of our daily lives, powering our cell phones and portable computers, we naturally want to spend less time waiting for batteries to charge up. This has prompted the search for ultrafast batteries. We would like batteries that can cycle at high currents, either discharging or charging in no time. Perhaps you’d like to charge your cell phone in under a minute, or you’d like to charge your EV in the same few minutes it takes to fill up with gasoline.

Either way, fast batteries are an engineering challenge. A good way to think of this is that it’s fairly easy to make a small battery that can cycle rapidly, but as a battery becomes larger, approaching the size it takes to power your phone or car, it gets more challenging. The way to understand this is to look at dimensional analysis.

Dimensional analysis example

Dimensional analysis is the engineering concept used to understand the scale or size of something, and was discovered by Galileo. Basically, to make size not matter, you have to eliminate all dimensionality in a problem. To do this you multiply/divide the important constants in the problem to make the dimensions cancel out.

Up above is a dimensionless number for a structure, which involves: the yield strength and density of the structure materials, the gravitational constant (gravity pulls down on the structure), and the structure size, which is L, a length like the height. Consider this: is a matchstick model of Notre Dame Cathedral a fair model of the real Notre Dame cathedral? And if so, does it mean you could make the real Cathedral out of wood too?

The answer is no. The matchstick model is not at all like the real Cathedral, because while size does change between the two, gravity does not. A successful matchstick model means you could build the real Cathedral out of wood … only on a smaller planet with a lower value of g.

Dimensional analysis of a battery

Dimensional analysis of a battery is similar to that of the Cathedral above. Imagine a small research-scale battery you might work with in a lab, and then imagine a practical battery based on it. The practical battery has been developed and scaled-up to provide the power and energy required by the application. Scaling up a battery almost always involves thickening the electrodes, and we will call this “increasing L.” The important length scale of an electrode is usually the thickness in the same dimension as current flow.

I’ve written previously about reaction rate distributions in battery electrodes (here and here). The dimensionless number δ (or John Newman’s number) tells you how balanced the reactions in a battery electrode are. When L increases, it tells you that something else has to decrease, like current I, if you want to keep δ the same. This means in general a small battery will charge fast and a large battery will charge slowly.

This is unless the other parameters in δ change accordingly to keep behavior the same … for example the porosity could be increased and that would increase the pore conductivity or κ and therefore decrease δ. But usually this goes in the opposite direction: as you scale up typically you want to achieve higher active material loading, pushing you to decrease porosity and thus decrease κ and increase δ. In fact, almost every decision you make during scale-up forces you to increase δ overall.

For this reason, the very first research decision you should try to make is to set L at the same value in your small battery that you will need in the final device. That way it becomes easier to understand scale-up, and you can extrapolate research results to real-world situations. When analyzing a fast battery, first check L and see whether scale-up will require it to increase.

In situ electrochemical microdiffraction

The high energy battery characterization I’ve been publishing about recently isn’t the only in situ technique that can shed light on battery materials. Combining electrochemical techniques with microdiffraction can tell you a lot about the composition of an interface between a battery material and electrolyte. Microdiffraction was developed at the National Synchrotron Light Source (NSLS) by Ken Evans-Lutterodt. It’s a kind of X-ray diffraction or XRD. The beam size is extremely small though, on the micron scale, and that’s why it’s described as “micro.”

microdiffraction setup small

We designed a flow cell that allows X-rays to hit an interface that is electrochemically active and has an electrolyte flowing past it. The X-ray beam penetrates the cell through a thin polyethylene window, and here the cell is only 150 μm thick, meaning even relatively low energy photons get through. The beam size is remarkably small: a small oval 2 x 5 μm, and the flow cell can be moved with sub-micron precision to focus the beam on the interface while a metal layer is plating there. The metal diffracts the beam, and an area detector on the other side records circular diffraction patterns. The ring pattern tells you what metals are in the diffraction spot, and their atomic spacing.

Preliminary designs for the small flow cell are shown below in panel (a), all of which ended up being too large or unwieldy in some way. The cell would have to fit in several beamlines at NSLS, and at one in particular it would have to have freedom to rotate 60 degrees without bumping anything. Taking into account the flow tubing and electrical wires, the fit would be tight. The first design, far too long and held together by binder clips, looks comical compared to the final design shown in (b). This cell has a paper-thin flow channel carved with a laser. The channel (c) is placed in the compression rig and screwed together (d).

flow cell designs small

My lab book from the first visit to the beamline shows what kind of thing I was trying to see. I wrote “Fantastic! See zinc disappear first locally on XRD then globally by E.” (And apparently this first worked at about 7:42 PM.) What’s going on is this: zinc is on the anode tab, much as it would be in a battery, then you dissolve the zinc to discharge the battery. When all the zinc is gone, the cell potential (E) will shoot up to high voltage. But that is macroscopic, meaning an average over the entire anode. By focusing the beam on a particular microscopic spot on the anode, you see it dissolve there first, giving you an insight into that small spot in contrast to the entire anode.

xrd micro-macro small

At CUNY we discovered that bismuth can be used to level zinc, but the mechanism wasn’t immediately clear. Using microdiffraction to scan through a zinc layer while it was being plated with bismuth gave a fascinating profile of the two metals, shown below. The XRD signal from the primary reflections of both Bi (012) and Zn (101) were plotted, along with their ratio. The layer was about 52 μm thick. Near the anode tab at 0 μm, the layer was bismuth-poor. Traversing through the layer toward the electrolyte interface, the composition became richer in bismuth, marked by the black arrow. Thus bismuth acts as a metal surfactant on zinc. (Published here.)

microdiffraction Bi-Zn ratio

At the very edge of the layer (shown by the green arrow), from 35 to 50 μm, the composition was almost entirely bismuth. The reduced bismuth signal there suggested this section could have the structure of a thin bismuth penumbra decorating the denser layer below. Since this data was collected in situ, this decoration might be a temporary structure present during electroplating, which is altered or destroyed by removing the layer from the electrolyte.

Modeling porous electrodes: Part 2

A secondary current distribution model considers:

  1. Ohm’s law resistance, and
  2. kinetic charge-transfer resistance

while resistance related to concentration variations is ignored. Beginning with the equations given in Modeling porous electrodes: Part 1, the following can be written:

Porous 2 equations

Eq 1 is conservation of charge; Eq 2 is some expression of electrochemical reaction kinetics; and Eqs 3 & 4 are Ohm’s law for the solid and liquid phases. The boundary conditions are such that a current density of I is being produced by the electrode. The liquid phase potential φ2 is arbitrarily set to 0 V at x = 0. The specific expression for the electrode kinetics (Eq 2) needs to be specified. The concentration-independent Butler-Volmer expression can be used:


The left hand side of this expression is the transfer current, with units of A/cm3, and gives the amount of electrochemical reaction occurring at any point. The right hand side has two components: the anodic and cathodic kinetic terms. The downside of the Butler-Volmer equation is its complexity. Finding an analytical solution to the above set of differential equations requires a more simplified kinetic expression. One possible simplification is to assume the overpotential (φ– φ2) is highly negative. This means only the cathodic term in the Butler-Volmer equation need be considered:


The right hand side of this expression is a form of the Tafel equation. (An analogous anodic form can be used when overpotential is highly positive.) Another possible simplification is to assume the overpotential (φ1 – φ2) is small. In this case both anodic and cathodic terms are important. Substituting the first two terms of a Taylor series for the exponentials results in:


This linear kinetic expression is valid only at low currents. Which approximation of the kinetic expression is appropriate depends on the conditions of interest. Choosing the following values for physical parameters:

  • electrode area per volume, a = 23,300 cm-1
  • transfer coefficients, αaαc = 0.5
  • exchange current density, i0 = 2 x 10-7 A/cm2
  • current density, I = 0.1 A/cm2
  • length, L = 1 cm
  • electrolyte conductivity, κ = 0.06 S/cm
  • electrode conductivity, σ = 20 S/cm

we assume that the Tafel approximation for kinetics will be valid, because the current density is much larger than the exchange current density. Solving the set of equations 1-4 for both Tafel and linear kinetics gives the results below:

 Porous electrode current

Porous electrode potential

The Tafel kinetic expression predicts that current exchange from liquid to solid phases (ionic current to electronic current) will be concentrated near x = 0, the location closest to the counter electrode. There (φ1 – φ2) will be near 300 mV, falling away further into the electrode. In contrast, the linear kinetic expression predicts a more even exchange of current through the electrode, and much higher values of (φ1 – φ2). This is because the linear expression is a softer function of overpotential than the exponential one. The Tafel approximation is clearly the more appropriate in this case because (φ1 – φ2) » RT/F which is 25.7 mV at room temperature.

2015-03-04 taf-lin trans

Plotting the transfer current di2/dx shows that in reality the electrochemical reaction is concentrated in the front 10% of the electrode. Linear kinetics tend to result in more uniform current distributions, but for this to be the case i0 > I will need to hold.