If you connect a lamp to a lithium battery, current flows and the lamp starts to glow. But why does this actually happen? Why does the voltage drop when the battery is discharged? What does this have to do with the concentration of Li-ions? Why does the type of electrode affect the capacity of the cell? This article provides answers.
Lithium-based cells – whether solid-state battery or conventional Li-ion battery – are basically similar in structure. There are two electrodes (positive and negative) with a separator between them. When charging, ions migrate from the positive side (cathode) to the negative side (anode) and when discharging, the ions migrate back again. Because the separator is impermeable to electrons, the electrons instead travel across a connected load, e.g. a lamp, and cause it to light up (more on the construction of solid-state batteries in particular can be found here).
This description can be used to explain why a current flows in the load, but it is not sufficient to understand where this energy comes from. For this, it is necessary to delve deeper into the functioning of the cell.
Voltage window of batteries
First of all, it should be clarified why a voltage between the positive and negative pole can be measured. The voltage window of lithium-based batteries is defined by the partial reactions at the anode and cathode and depends accordingly on the reactions taking place there. The voltage that can be measured on a battery at its poles is the difference of the voltage generated at the respective electrodes:
The voltage at the anode and cathode is not a fixed value, but depends on the state of charge of the cell. However, fixed values are often given for the electrodes in the literature (e.g. 3.9 V for LCO, cf. [1]). These usually correspond to the average voltage.
Figure 1 shows how the resulting cell voltage is derived from the anode and cathode potential (shown on the example cell LCO|Graphite). The x-axis shows how much lithium is proportionally bound in the electrodes. For an (ideal) full battery x=1, for an empty battery x=0.
Figure 1: Voltage of an LCO|graphite cell divided into anode and cathode potential. Typically, only 70 % of the Li-ions are extracted from the cathode (dashed line) Material selection untypical for solid-state batteries, but possible in principle, Own illustration according to [2].
The measurable voltage at the positive and negative terminals of the battery results from the chemical reactions that the lithium undergoes with the electrodes. This will be explained in more detail using the example of an LCO cathode. Figure 2 shows the discharge process of an LCO|graphite cell. This is a lithium ion cell with liquid electrolyte. The design is in principle also possible with solid-state batteries, although LCO and pure graphite are atypical as electrode materials and instead further developments of these materials (e.g. silicon graphite as anode and NMC811 as cathode) are used.
Figure 2: Discharge reaction of a lithium-ion battery with liquid electrolyte. The voltage is generated by the charging and discharging process of the Li-ions from the anode and cathode. Reactions shown also apply to solid-state batteries, although the choice of material is atypical here, Own illustration.
During discharge, the Li-ions migrate from the anode to the cathode. LCO is a cathode with a layered structure. The lithium intercalates between the cobalt oxide layers during discharge. The reaction equation of the lithium with the cobalt oxide is as follows:
The externally measurable voltage arises due to the intercalation reaction of the lithium into the individual layers of the layer oxide and the energy released in this exothermic process. With the help of the so-called Nernst equation, the resulting voltage of a half cell can be calculated with the aid of the substance concentrations in the cell:
with
U0,red: Electrode potential (can be read from the electrochemical voltage series tables).
R: Universal gas constant
T: Temperature (in Kelvin)
ze: Number of transferred electrons (lithium has only one valence electron, therefore here 1)
F: Faraday constant
αRed , αOx: Concentrations of the respective redox reactants
The concentration of the redox reactants changes with the state of charge of the electrode. The resulting voltage of an electrode thus depends essentially on the electrode potential, which is corrected for the temperature and the state of charge. It should be noted that some secondary reactions also take place in a battery, which also have an influence on the resulting voltage, so that the above equation should only be used as a first approximation.
Because of the strong dependence of the Nernst equation on the electrode potential, an attempt is made to select elements that have the highest electrode potential here (see Figure 3). Elements further to the right in the periodic table achieve higher ratios here because the ionic radius of the elements decreases and the electrons are more strongly attracted to the nucleus. The stronger nuclear forces then result in a higher electrode potential.
This connection also explains why LCO (LixCoO2) and NMC811 are used as cathode materials. Within the transition metals, these are the compounds with the highest half-cell voltages (see Figure 3) [4].
Figure 3: Electronegativity within the transition metals, partly own illustration.
Limitations of the voltage window
The permissible voltage range of a cell is not only influenced by the electrodes. The achievable voltage is limited by the electrochemical window of the electrolyte used. In particular, liquid electrolytes cannot cope with a cell voltage above 4.5 V, since parasitic reactions of the cathode with the electrolyte occur and lead to the electrolyte slowly decomposing [5]. Solid-state batteries may be able to break this limitation in the medium term. Oxide-based electrolytes, for example, have a particularly wide voltage window, and sulfide-based electrolytes could also be able to tolerate higher voltages with additional protective layers [6].
A second important limitation of the voltage window is that it is usually not possible to use the complete physical voltage window of the battery. For the LCO cathode, it is not possible to dissolve more than 70 % of the lithium out of the cobalt layers, as this would weaken the mechanical structure of the cathode, leading to accelerated aging. Therefore, the voltage is limited to 4.2 V for LCO cells compared to Li/Li+ [7]. On the anode side, it is also generally not possible to remove all the lithium ions, so that some of them remain behind here as well, thus reducing the maximum achievable capacity.
Determination of the capacity of the battery
In order for a cell to deliver the maximum capacity, the anode and the cathode must be dimensioned in such a way that during the charging process all Li-ions that exit the cathode also find a place in the anode structure for storage. The ratio of the size of the anode to 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 for each Li-ion from the cathode there must also be a place in the anode, the size ratio is N/P≈1. However, lithium ions find it difficult to always find a place in the anode. Instead, the Li-ions tend to deposit on the anode (Li plating), especially during fast charging, because they cannot find free places in the anode structure quickly[8]. Since Li plating is one of the main damage mechanisms of cells, the proportion of the anode is increased somewhat (N/P≈1.04-1.2) [9] so that the ions do not have to search so long to find a free place.
Figure 4: Procedure for calculating the theoretical capacity of the cathode materials, own illustration
The capacity of the respective active materials is usually given in Ah⁄kg and can be calculated (see calculation scheme Figure 4). Only the active material is considered for the calculation. Chemical aids, contacting surfaces, protective layers, etc. are ignored in the calculation of the theoretical capacitance of the electrodes. For the calculation, the weight of the electrode material is first determined in kg⁄mol. The value here can either be calculated using the molar masses, or taken from look-up tables. For LCO, the specific mass is 0.09788 kg⁄mol . In a second step, the Avogadro constant can be used to calculate how many molecules there are in one kg of the electrode material (for LCO, this is 6.15*1024 atoms per kilogram).
As an alkali metal (element of the first main group), lithium has only one electron that can participate in a chemical reaction. Each electron has a negative elementary charge of e–. Accordingly, a lithium atom can emit exactly one elementary charge e–.
To calculate the capacity, it must now be taken into account that for each Li-ion, one electron passes over the connected load during discharge. The capacity is therefore the product of the amount of charge carried by an atom multiplied by the number of atoms. For LCO, this results in a capacitance of 274 Ah⁄kg. The capacitance of other cathode materials and also of anode materials can be calculated in the same way. Figure 5 lists the calculated theoretical energy densities for the most important cathode materials.
Figure 5: Theoretical calculation of the cathode capacitance
The calculated values represent the theoretically achievable energy densities, but are generally not very close to practical values. With LCO, for example, only part of the lithium can be removed during the charging process, so that the theoretical capacity is not fully utilized and significantly lower values are achieved in practice. Nevertheless, the calculated figures provide a good indicator for comparing different active materials with each other.
Conclusion
The answer to the question of where the energy from a Li-cell actually comes from is thus clear: The cause is the redox reaction that takes place more or less reversibly in the battery during charging and discharging. Due to the structure of the cell, electrons are forced to migrate to the anode via the charger during charging. The resulting charge shift causes the Li-ions to also migrate to the anode. When discharging, the process reverses and current flows across the connected load and power is transferred. The voltage generated by the battery at a given state of charge can be calculated using the Nernst equation and depends mainly on the concentration of Li-ions on the electrodes. The more Li-ions migrate to the cathode side, the higher their concentration at the cathode and the cell voltage drops accordingly.
How much energy a battery can supply depends on the battery’s capacity. The capacity is a material-specific variable and can be calculated directly from the material data using simple equations.
All calculated parameters represent theoretical (maximum) values which are not achieved in practice. The voltage is limited by the electrolyte, a complete utilization of the capacity would affect the mechanical stability of the cathode. Also, slightly more anode material is always used than absolutely necessary to prevent parasitic deposition of lithium. It is the goal of a good design process to weigh all of these effects to obtain a practical cell capable of surviving many hundreds of cycles in automotive use. The best cell is always a compromise.
Sources
[1] Park, J: Principles and Applications of Lithium Secondary Batteries, Department of Chemical & Biomolecular Eng., Korea, 2012, S. 28
[2] Qnovo: The science behind why the battery vendors are hitting the wall, 2014, https://www.qnovo.com/blogs/why-battery-vendors-are-hitting-the-wall
[3] J. Goodenough, K. Park: „The Li-Ion Rechargeable Battery: A Perspective“, American Chemical Society, 2013
[4] Liu, C., et al.: “Understanding electrochemical potentials of cathode materials in rechargeable batteries”, Materials today, 2016
[5] Yang, L.; Ravdel, B. ;Lucht, B.: „Electrolyte Reactions with the Surface of High Voltage LiNi0.5Mn1.5O4 Cathodes for Lithium-Ion Batteries“, Electrochemical and Solid-State Letters, 2010
[6] Fraunhofer Institute for Systems and Innovation Research ISI: Solid-State Battery Roadmap 2035+, Karlsruhe, 2022
[7] Korthauer, Reiner : Handbuch Lithium-Ionen-Batterien, Frankfurt, 2013
[8] TYCORUN: A comprehensive guide to battery cathode and anode capacity design, 2022, https://www.tycorun.com/blogs/news/a-comprehensive-guide-to-battery-cathode-and-anode-capacity-design
[9] TYCORUN: Design anode to cathode ratio of lithium-ion battery, 2023, https://www.takomabattery.com/anode-to-cathode-ratio/
[10]: Park, J: Principles and Applications of Lithium Secondary Batteries, Department of Chemical & Biomolecular Eng., Korea, 2012, S. 28
