UHPC 101 Part 2 – Coulombic Inefficiency Per Hour (CIE/hr)

Introduction

In Part 1 of UHPC 101 we discussed Coulombic Efficiency (CE) and introduced it as a critical metric for quantifying cell performance. In general, the closer the CE is to 1, the longer that cell will last. Despite the importance and usefulness of CE, some important considerations are needed to enable fair comparisons of cells cycled under different conditions because cell degradation depends on both time and cycle number. Some degradation mechanisms, such as reactions of electrolyte components, will occur even if a cell is sitting on a shelf and is not being cycled. The time dependence of reactions within a Li-ion cell presents a challenge for meaningfully comparing the CE, which measures these reactions, of cells where cycles take a different amount of time; cells with cycles that take more time will experience more reactions per cycles. In this way, CE is understood to be a function of both cycle number and time.

Coulombic Inefficiency Per Hour (CIE/hr)

In this second post of the UHPC 101 series, we explore how to compare the CE of cells cycled differently, whether at different rates (currents) or to different states of charge (voltages). It is important to understand the time dependence of CE – as explained above, time-dependent degradation reactions within the cell will lead to higher CE values for a cell cycled faster, compared to the same cell cycled slower.

To expand the usefulness of CE and to make the best decision for your product or technology application, CE must be normalized for time, broadening the scope of applicability. This is Coulombic Inefficiency per hour (CIE/hr).

As a practical example, consider two identical cells cycling under the same current but to different upper cut-off voltages: 4.1 V and 4.3 V. The cell cycling to 4.1 V will complete a cycle in less time than the cell cycling to 4.3 V. The CE must be normalized for time to fairly compare these two cells.

To help illustrate the time-dependence of certain reactions within a Li-ion cell, consider the following analogy:

You’re sitting on a patio on the Halifax waterfront with a refreshing Nova Scotian craft beverage in front of you. But every time you take a drink, your glass leaks (just like the leaky bucket from the first post). Of course, the faster your drink cycle (pick up glass – drink – put the glass down), the less beverage you lose. The leaking rate, however, doesn’t change because you are drinking faster – you're just allowing less time for the leak!

Coulombic+Inefficiency+Per+Hour_analogy

The CE of a Li-ion cell is always less than 1, partly due to unwanted reactions that consume Li and lead to capacity loss over time. Generally, reactions occur at some rate, thus with more elapsed time, there is more time for these unwanted reactions to occur.  If the CE of two cells is measured under different cycling rates, the cell under higher rate may experience fewer Li-consuming reactions per cycle because less time elapses per cycle. Coulombic inefficiency per hour (CIE/hr) normalizes the CE by the time per cycle. The Coulombic inefficiency (CIE) is defined as 1 – CE, so conversely to CE, better cells will minimize CIE. Measurements at higher rates, which take less time, have smaller CIE (larger CE), thus when dividing by the time per cycle, the CIE is reduced by a smaller factor.

Similarly, measurements at lower rate take more time per cycle and have larger CIE, so dividing by the time per cycle reduces the CIE by a larger factor. This way, the CIE/hr allows comparison of CE measurements of cells cycled under different rates provided the electrochemical reaction mechanisms do not depend on current.

Consider again the two identical cells cycled to 4.1 V and 4.3 V under the same current. If the CIE/hr of each cell was the same, it would be an indication that the unwanted reactions in the cell are not worsened by cycling to higher voltage. Such inferences can be very useful for determining cell operability windows given a set of application constraints. In some chemistries, such as Silicon-containing anodes for example, degradation mechanisms depend on both time and the number of cycles; a greater number of cycles in the same amount of time can increase the CIE/hr. Understanding CIE/hr measurements can help gain insight into the degree of cycle-based versus time-based degradation mechanisms.

To illustrate CIE/hr in action, the image below depicts two sets of cells cycled at the same temperatures and voltage limits at low rates of C/32 (black) and C/16 (red). The cells running at the slower rate have a lower CE when plotted vs cycle. However, when CIE/hr is plotted vs the time the cell is being tested for, we can see the unwanted mechanisms appear to be identical between the cells regardless of cycle number.

Coulombic+Inefficiency+Per+Hour_two_cell

In summary, careful analysis of CE and CIE/hr from UHPC data can be used to determine the effects of various operating conditions on unwanted mechanisms occurring in cells. With the accuracy and precision of UHPC, these metrics give insight into how cells respond to environmental conditions, voltage windows, and different applied rates* with respect to both time and cycle number. These precise tests using UHPC can be done in only 2-3 weeks, enabling better decisions sooner than traditional cycling.

In the coming posts we dive deeper into the underlying components of coulombic inefficiency: Capacity Fade and Charge Endpoint Capacity Slippage, what causes them, and how understanding these mechanisms can help you develop and select better cells!

Disclaimer: UHPC measurements to probe different failure mechanisms at various operational conditions require careful consideration of the rate being applied to the cell due to the effects of kinetics. Kinetically limited cells are subject to additional failure mechanisms that influence CE such as lithium-plating and self-heating, as well as lithium concentration gradients within the electrodes – any CE measurement to specifically probe the electrochemical stability of materials within the cell must be performed with sufficiently low rate so that there are no apparent capacity losses due to kinetics.

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