The maximum charge an electrode material can store, expressed per unit mass. It is calculated as Q = nF/(3.6M) mAh/g; for graphite it is 372 mAh/g.
Japanese name: 理論容量
Theoretical capacity appears in 3 practice questions across 1 topic, including Battery and energy materials.
Field: Battery and energy materials
When 1 mol of electrode material reacts and exchanges n mol of electrons, the charge passed is nF coulombs (F is the Faraday constant, 96485 C/mol). Dividing by the formula weight M gives the charge per unit mass, and converting with 1 mAh = 3.6 C gives Q = nF/(3.6M) mAh/g. For graphite, 1 mol of C₆ (72.06 g/mol) takes up one Li⁺, giving 372 mAh/g; for LiCoO₂, extracting all of the one Li gives about 274 mAh/g. The value changes depending on which mass is used in the denominator, so it is important to check which state's mass the capacity is quoted per.
Not all of the calculated theoretical capacity can necessarily be used. In layered LiCoO₂, extracting more than about half the Li destabilizes the crystal structure and degradation proceeds through oxygen release and phase transitions, so practical capacity has been limited to about 140–150 mAh/g, roughly half the theoretical value. Graphite and LiFePO₄, by contrast, can be used close to their theoretical values. On the first charge, an SEI film forms on the anode surface and some lithium is lost, so the capacity obtainable from the cell is slightly smaller still.
The energy stored in a battery is the product of capacity and voltage. The larger the potential difference between the positive and negative electrodes, the more energy is stored for the same capacity. LiFePO₄ has a theoretical capacity of about 170 mAh/g, but its average voltage of about 3.4 V is lower than that of layered oxides (about 3.7–3.8 V), so its energy per mass is smaller. In addition, the whole cell includes the mass of the electrolyte, separator, current collectors and casing, so the energy density of a cell is far smaller than the value calculated from the active materials.
Answer: C. About 372 mAh/g
One mole of C₆ (72.06 g) takes up one mole of Li⁺ and one mole of electrons, so the stored charge is 96485 C. The capacity per mass is Q = nF/(3.6M) = 1 × 96485 / (3.6 × 72.06) ≈ 372 mAh/g. About 339 mAh/g uses the mass of LiC₆ including Li (78.99 g/mol) in the denominator; anode capacity is normally expressed per mass of lithium-free graphite. About 2230 mAh/g is the mistake of assuming one lithium per carbon atom. Real graphite anodes are used at about 350–360 mAh/g, close to the theoretical value, and materials such as silicon are being researched to achieve higher capacity.
Answer: A. About 170 mAh/g
One mole of Li⁺ leaves one mole of LiFePO₄ and Fe²⁺ is oxidized to Fe³⁺, so one mole of electrons is transferred. The theoretical capacity is Q = nF/(3.6M) = 1 × 96485 / (3.6 × 157.8) ≈ 170 mAh/g. About 340 mAh/g counts two electrons in the reaction, but the change from Fe²⁺ to Fe³⁺ involves one electron. About 85 mAh/g divides by 2 somewhere along the way. LiFePO₄ can in practice deliver around 160 mAh/g, close to the theoretical value, but its average voltage of about 3.4 V is relatively low, so its energy per mass is smaller than that of layered oxide cathodes.
Capacity alone does not decide it. Voltage, cycle life, volume change, safety and cost also matter. Silicon has about ten times the theoretical capacity of graphite, but its large volume change makes it difficult to use on its own.
mAh/g is the charge stored per unit mass, and Wh/kg the energy stored per unit mass. Multiplying charge by the average voltage gives energy, and the value of mAh/g × V is numerically the value in Wh/kg.
The capacity of the cell is set by the electrode with the smaller capacity. In real cells, the anode capacity is generally designed to be slightly larger than the cathode's so that lithium metal does not plate on the anode.
The theoretical capacity is Q = nF/(3.6M) = 1 × 96485 / (3.6 × 157.8) ≈ 170 mAh/g.
For the olivine cathode material LiFePO₄, assuming all the …Si alloys with lithium, and when it reacts as far as Li₁₅Si₄ at room temperature its theoretical capacity is about 3600 mAh/g per mass of Si, about ten times that of graphite (372 mAh/g).
Which statement about silicon (Si) as an anode material is …Solid electrolyte Layered rock salt structure Olivine structure Polymer electrolyte fuel cell Shockley–Queisser limit Spinel structure Thermoelectric figure of merit