1. Lithium ion Battery theoretical capacity calculation

2. ELECTRON, ION AND COULOMBIC ENERGY
The Motion of an ion in the electrolyte or of an electron in a wire is a transfer of definite amount of electricity.
The actual amount of electricity transported by a single electron or a monovalent ion is very small..
x Coulombs
According to Faraday’s law, 1 gram equivalent of any substance is equal to Coulombs, I.e., if the ion is monovalent the total charge is Coulombs and if bivalent the charge is twice of this amount.

3. ELECTRON, ION AND COULOMBIC ENERGY
1 Amp : 1 Coulomb / Sec
1 Amp-Sec. : 1 Coulomb
1 Amp. Hr. : 3600 Coulomb
1 Faraday : Coulombs
96490/3600 = 26.8 Ah
i.e. for 1 electron transfer the coulombic energy is 26.8 Ah

4. Lead acid Li-ion For Lead Acid Battery System
ELECTRON, ION AND COULOMBIC ENERGY
Lead acid
For Lead Acid Battery System
No. of electrons transfer :2
Pos. PbO2 Molecular Wt : 239 g
Neg. Pb Molecular Wt. :207 g
For a 2e- transfer, Coulombic energy is
2 x : 53.6 Ah
Li-ion
For Li-ion Battery System
No. of electrons transfer :1
For a 1e- transfer, Coulombic energy is
26.8 Ah

5. ELECTRON, ION AND COULOMBIC ENERGY
Pb acid:
Pos. active material (PbO2) required to deliver 1 ampere hour (239/53.6) : 4.46g
Neg. active material (Pb) required to deliver 1 ampere hour (207/53.6) :3.862 g
Electrolyte (H2SO4): 3.68 g/Ah
Li-ion:
Pos. active material ( LiFePO4) required to deliver 1 ampere hour (157.75/26.8) :5.886g/Ah
Neg. active material (C6) required to deliver 1 ampere hour (72.060/26.8)
:2.689 g
Li:6.941,Fe:55.845,P:30.974,O:63.998

6. The theoretical capacity of a material can easily be calculated from Faraday’s 1st law of electrochemistry
which states that 1 gram equivalent weight of a material will deliver96487 coulombs (or 26.8 Ah).
For LiMn2O4 the equivalent weight (M) is g/mol, giving a theoretical capacity of: 26.8/180.8 = 148 mAh/g
Inthe same way, the theoretical capacity of Li2Mn2O4 can be determined to 285 mAh/g, ifthe whole charge/discharge range is exploited

7. The thermodynamic quantity describing the change in energy as a function of changes in Li concentration in the host matrix is the chemical potential ( µ ), defined as
µ= ƏG
Ə x
where G is the Gibbs free energy and x is the number of inserted Li atoms. The change in free energy can also be expressed as
where n is the number of electrons in both electrode-reactions δ in the cell-reaction above), F is Faraday’s constant, and E is the potential difference between the electrodes. By combining (1) and (2), we get the relation between electrical and chemical energy in the system:
-δFE=µc --µa
where µc c and µa are the chemical potentials of the lithium ions in the cathode and anode, respectively.
ΔG = -nFE = -δFE

8. Ampere-hour (Ah)
capacity is the total charge that can be discharged from a fully charged battery under specified conditions.
People also use Wh (or kWh) capacity to represent a battery capacity. The rated Wh capacity is defined as
Rated Wh Capacity = Rated Ah Capacity × Rated Battery Voltage:
Power : energy by second ,watt
W=A×V=Current × Voltage
Energy :power multiplied by time
WH=Ah × V=Capacity × Voltage
Capacity : Current × time Ah

12. Cathode material
Discharge Voltage V vs .Li0
Theoretical capacity (mAhg-1)
True density (g cm-3)
Diffusivity (cm2s-1)
LiMnPO4
4.1
171
3.43
10-7
LiFePO4
3.4
170
3.60
10-8
LiCoPO4
4.8
167
3.70
10-9
LiNiPO4
5.1
3.89
10-5
Li1.07Mn1.93O4
3.9
117
4.15
~10-10
LiAl0.05Co0.15Ni0.8O2
3.6
265
4.73
~10-8
LiCoO2
274
5.05
Source Theoretical evaluation of high-energy lithium metal phosphate cathode materials in Li-ion batteries –JPS -165(2007)

13. Other Cathode Materials
1. Ohzuku, T.; Brodd, R. J., J.Power Sources 2007, 174, (2), ; 2. Amatucci, G. G.; Pereira, N., J. Fluorine Chemistry 2007, 128, (4), ; 3. Howard, W. F.; Spotnitz, R. M., J. Power Sources 2007, 165, (2), 37