The most basic efficiency of a rechargeable cell is the coulombic efficiency. Note that in contrast to the faradaic and current efficiencies that were defined in Chapters 1 and 3, this coulombic efficiency refers to a battery that undergoes a complete charge–discharge cycle.
(7.21)
Why would the number of coulombs be different for charge and discharge? The principal reason is that secondary reactions occur; that is, some of the current goes to undesired reactions. For example, when charging a NiCd battery, gases may be evolved as a side reaction. Although it may be possible to recombine the gases (generated from electrolysis of water) in order to avoid loss of electrolyte, the coulombs used to generate the gases are not available for power generation on discharge. There can also be irreversible losses such as the formation of the solid electrode interphase (SEI) in lithium cells. Here, the electrolyte reacts with lithium in the negative electrode, making the reacted lithium unavailable for cycling.
Typical values for coulombic efficiency are 95% or greater for many rechargeable cells; and acceptable values depend on the particular chemistry involved. The coulombic efficiency must be very close to one to achieve reasonable battery life for rechargeable cells when the side reactions are irreversible and result in a loss of active material (see Problem 7.18 for the lithium-ion cell).
In some cases, side reactions can provide overcharge protection for a battery. For example, for an acid-starved lead–acid battery, the dominant side reactions during overcharge are
and
The cell is designed so that the evolved oxygen can move rapidly through the separator in the gas phase to the other electrode where it reacts to form water. This recombination prevents loss of electrolyte and damage to the cell due to overcharging.
A second efficiency of interest is the voltage efficiency. The difference between the potential during charging and discharging determines the voltage efficiency of a rechargeable cell. Any polarization of the cell due to ohmic, kinetic, or concentration effects will cause the difference to increase and the efficiency to decrease. Therefore, the voltage efficiency decreases with increasing current density due to the increased irreversible losses at the higher current. Similar to the coulombic efficiency, the voltage efficiency for a rechargeable cell applies to a cell undergoing a complete charge–discharge cycle. Voltage efficiency is defined as the ratio of the average cell voltage during discharge and charge.
The average voltage is determined by integrating over time. For example, during discharge,
The energy efficiency is the product of the coulombic efficiency and the voltage efficiency, and represents the so-called round-trip efficiency,
(7.23)
The energy efficiency will be lower than the coulombic efficiency since the voltage efficiency is less than 100%. The typical round trip efficiency of a secondary cell can be near 90% for rechargeable batteries. This efficiency will, of course, depend on the rates of charge and discharge.
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