Charge retention refers to the amount of charge, usually expressed as a percentage of capacity, remaining after a cell is stored for a period of time and not connected to an external circuit. Self-discharge describes the mechanism by which the capacity of the cell is reduced. Rates of self-discharge can vary dramatically—a 10% loss in capacity may take 5 years for a lithium primary cell, but only 24 hours for some nickel-based cells. Comparing two secondary cells, we see that self-discharge rates also vary widely with chemistry. For example, a Ni-MH cell may discharge 30% per month, whereas lithium-ion cells have rates closer to 5% per month. For a secondary rechargeable battery, self-discharge can be further characterized as either reversible or irreversible. Irreversible self-discharge contributes to capacity fade, which is discussed further in Section 7.9.

The rate of self-discharge is an important design requirement for any battery. A low rate of self-discharge is a critical feature of a primary cell. The rate determines the amount of time that the battery remains useable. Many primary batteries are stored for long periods of time before being put into service. Others are in use, but only needed for backup power, for example, memory in electronic circuits. A service life of 10 or 20 years is not uncommon. The need of some applications for extremely long shelf life is the principal reason that reserve batteries have been developed. Some reserve batteries may be required to be in place, but not in use for a decade or more. As noted previously, the rates of self-discharge are strongly dependent on the cell chemistry, but cell design and manufacturing processes can be specified to reduce the rate of self-discharge—that’s the role of the engineer. There are many mechanisms that cause a cell to self-discharge. A few physical causes are discussed below as examples.

The easiest one to understand is an electronic short across the cell. A small short, though clearly undesirable, can be introduced in the manufacturing process of both primary and secondary cells. More often shorts result from use. For instance, the plates of a lead–acid cell can swell and shrink during operation, putting pressure on the separator. Mechanical shock could also cause the two plates to touch. In extreme cases, dendrites of lead (tree formation) can penetrate through the separator. In each instance, an electronic path between the two electrodes is established inside the cell. The rate of self-discharge is simply

(7.24)

A key difference between an external short and an internal short is that all of the resistive heating associated with an internal short is inside the cell. This feature has important implications for thermal runaway, a safety concern for lithium-ion and some lead–acid cells.

A second source of self-discharge is a shuttle mechanism. For instance, in either NiCd or Ni metal-hydride cells, ammonium hydroxide can be formed from the breakdown of a polyamide separator. This impurity contributes to self-discharge through a chemical shuttle mechanism as described below. At the positive electrode of the Ni-MH cell,

(7.25)

Transport of nitrite to the negative electrode yields

(7.26)

These two reactions combine to yield

(7.27)

which is the overall reaction for the discharge of a Ni-MH cell (see Table 7.1). Ammonium ions produced at the negative electrode diffuse back through the separator to the positive electrode, where they are converted to nitrite as the cycle continues. These reactions and transport between electrodes result in a chemical short, which discharges the cell.

An analogous shuttle involving the redox reaction of an impurity metal, M,

can also contribute to self-discharge if the potential for this reaction lies between that of the positive and negative electrodes. Under such conditions, the metal will be oxided at one electrode and reduced at the other, forming a chemical short (see Problem 7.25). This possibility emphasizes again the need to minimize impurities in cells during manufacturing.

A third and common mechanism for self-discharge is corrosion. Often one or both of the electrodes are thermodynamically unstable in the charged state. For instance, two of the many possible self-discharge reactions for the lead–acid cell are grid corrosion on the positive electrode and evolution of hydrogen on the negative electrode. Note that the lead oxide in the positive plate is supported on a grid of Pb.

Whether controlled by transport or kinetics, rates of self-discharge are expected to increase strongly with temperature, and this phenomenon is generally observed.

ILLUSTRATION 7.7

A Ni-MH cell is constructed with a separator thickness of 200 μm. The effective diffusion coefficient of ammonium hydroxide in the electrolyte is 3 × 10⁻¹⁰ m²·s⁻¹, and the concentration of ammonium hydroxide is 1mM.

1. Sketch the concentration profiles of NH₄⁺ and NO₂⁻ across the separator assuming the reactions at the electrodes are fast.If reactions are fast, the concentration of reactants will be zero at electrode. The profile is linear with an average of 1 mM.
2. Calculate the rate of self-discharge using Fick’s law for diffusion.The integrated form of Fick’s law isThe flux is converted to a current density with Faraday’s law:
3. For a 0.6 A·h cell and a separator area of 0.05 m², estimate the time required to fully discharge the battery.