How the voltage and capacity of lithium battery are generated

Working principle of lithium battery

Lithium-based batteries, whether they are solid-state batteries or conventional lithium-ion batteries, the lithium ion battery structure are basically similar. There are two electrodes (cathode and anode) with a lithium ion battery separator in between. When charging, ions migrate from the cathode to the anode, and when discharging, the ions migrate back again.

Battery voltage window

To know how the voltage of a lithium battery is generated, firstly, it is necessary to clarify why the voltage between the cathode and anode can be measured. The voltage window of a lithium battery is defined by the partial reactions at the cathode and anode and accordingly depends on the reactions taking place there. The measurable voltage across a battery is the difference between the voltages produced by the individual electrodes:

UOC = U anode – U cathode

The voltage of the cathode and anode is not a fixed value, but depends on the state of charge of the battery. Usually, however, a fixed value for the electrodes (for example, 3.9 V for LCO) corresponds to an average voltage.

The figure below shows how the final cell voltage (shown on the example cell LCO | Graphite) is derived from the cathode and anode potentials. The x-axis shows the amount of lithium bound proportionally in the electrode. x=1 for (ideally) full battery, x=0 for empty battery.

The measurable voltage at the cathode and anode of the battery is produced by a chemical reaction between the lithium and the electrodes. This will be explained in more detail below taking the LCO (lithium cobalt oxide) cathode as an example. The figure below shows the discharge process of the LCO|graphite battery.

This is a lithium-ion battery with a liquid electrolyte. In principle, this design is also applicable to solid state battery, although LCO and pure graphite as electrode materials are atypical, and further developed materials are used, like silicon graphite as anode and NMC811 as cathode.

Battery voltage generation

The voltage is generated by the process of charging and discharging lithium ions at the cathode and anode. The reactions shown in the figure are also applicable to solid-state batteries, but the materials chosen here are not typical and are for reference only. During discharge, lithium ions migrate from the anode to the cathode. LCO is a cathode with a layered structure. During discharge, lithium intercalates between the cobalt oxide layers.

The reaction equation between lithium and cobalt oxide is as bellow:
CoO2 + e– + Li+ → LiCoO2

The generation of an externally measurable voltage is due to the intercalation of lithium in the layers of the layered oxide and the energy released during this exothermic process. Using the Nernst equation, the half-cell voltage can be calculated from the species concentration in the cell:

Ured = U(0,red) – (RT / (ze F)) * ln(αRed / αOx)
U0,red: electrode potential (can be read from electrochemical voltage series table)
R: universal gas constant
T: temperature (Kelvin)
ze: number of transferred electrons: number of transferred electrons (lithium has only one valence electron, so it is 1 here)
F: Faraday constant
αRed , αOx: the concentration of each redox reactant

The concentration of redox reactants varies with the charge state of the electrodes. Thus, the resulting electrode voltage essentially depends on the electrode potential, which is corrected for temperature and state of charge. It should be noted that some secondary reactions also occur in the battery, which also affect the resulting voltage, so the above equation should only be used as a first approximation.

Due to the strong dependence of the Nernst equation on the electrode potential, researchers try to select the element with the highest electrode potential (pictured below). Elements on the right side of the periodic table reach a higher proportion because the ionic radius of the element is reduced and electrons are more strongly attracted to the nucleus. Stronger nuclear forces lead to higher electrode potentials.

This connection also explains why LCO (LixCoO2) and NMC811 were used as cathode materials. Among the transition metals, these are the compounds with the highest half-cell voltages.

Voltage window limitations

The allowable voltage range of a battery is not only affected by the electrodes, but also limited by the electrochemical window of the electrolyte used. In particular, liquid electrolytes cannot withstand voltages exceeding 4.5 V because of parasitic reactions between the cathode and the electrolyte, resulting in slow decomposition of the electrolyte.

Solid-state batteries may be able to overcome this limitation in the medium term. For example, oxide electrolytes have a particularly wide voltage window, and sulfide electrolytes may also be able to withstand higher voltages with the addition of an additional protective layer.

A second important limitation of the voltage window is that the full physical voltage window of the battery cannot usually be utilized. For LCO cathodes, it is impossible to dissolve more than 70% lithium from the cobalt layer, as this would weaken the mechanical structure of the cathode and lead to accelerated aging.

Therefore, compared to Li/Li+, the voltage of LCO cells is limited to 4.2V. On the anode side, typically not all of the lithium ions can be removed, so some remain in the anode, reducing the maximum achievable capacity.

Calculation of battery capacity

For a battery to provide maximum capacity, the cathode and anode must be aligned so that during charging, all the lithium ions coming out of the cathode find storage in the anode structure. The ratio between the size of the anode and the size of the cathode is called the N/P ratio, where N describes the mass fraction of the anode and P describes the mass fraction of the cathode.

Since every lithium ion coming out of the cathode must find a place at the anode, the size ratio N/P≈1. However, it is difficult for lithium ions to always find a place at the anode. During fast charging, lithium ions tend to deposit on the anode (lithium plating), because they cannot quickly find free places in the anode structure. Since lithium plating is one of the main damage mechanisms of the battery, the ratio of the anode is slightly increased (N/P ≈ 1.04-1.2) so that the ions do not have to search for too long to find a free place.

The capacities of various active materials are usually given in Ah/kg and can be calculated. The calculation only considers the active material. The chemical additives, contact surface, protective layer, etc. are ignored in the calculation of the theoretical capacity of the electrode.

When calculating, first determine the mass of the electrode material (in kg/mol). This value can be calculated from the molar mass or obtained from a lookup table. For LCO, the molar mass is 0.09788 kg/mol. In a second step, Avogadro’s number can be used to calculate how many molecules are in a kilogram of electrode material (for LCO, it is 6.15*10^24 atoms per kilogram).

As an alkali metal (element of the first main group), lithium has only one electron that can participate in chemical reactions. Each electron has a negative elementary charge e–. Therefore, a lithium atom can release an elementary charge e–.

To calculate the capacity, it must now be taken into account that during discharge each lithium ion transfers one electron through the connected load. Therefore, capacity is the product of the charge carried by an atom and the number of atoms. For LCO, it results in a capacity of 274 Ah/kg.

The capacity of other cathode materials and anode materials can also be calculated by the same method. The table below lists the calculated theoretical energy density of a battery of the most important cathode materials.