Batteries

Primary Battery

Non-rechargeable battery, cheap and disposable e.g. Zinc Graphite, Alkaline, Lithium Iron Disulphide

Secondary Battery

rechargeable battery, designed for multiple used but with a limited lifetime such as Lithium-ion, Nickel-Cadmium, and Lead-Acid.

Anode

Electrode where oxidation occurs

Cathode

Electrode where reduction occurs

Gibbs Free Energy (Equation)

DG=-n*F*DE

Overpotential

Change in potential due to the loss or gain of electrons leading to a change in thermal level

Thermal Level

Average kinetic energy of a material

Standard Potential, E0

Potential above which a reaction will occur

Tafel Plot Relationship

i=a*exp(eta/b)

Arrhenius Equation

rate = A*exp(-Eact/RT)

Activation Potential, Eact

Potential above which reactants are converted to products, Eact=E-E0=eta

Butler-Volmer Equation

Butler-Volmer: Small Overvoltage

Linear, j=a+(a/b)*eta

Butler-Volmer: Intermediate Overvoltage

Tafel Plot: i=a*exp(eta/b)

Butler-Volmer: High Overvoltage

Mass transfer limit, Flick’s Law: j=flux=D* dCox/dx

Battery

Batch reactor with products and reactants contained

Extent of Reaction

opposite of state of charge

Sulphation

formation of insoluble lead sulphate on both electrodes blocking the active material

Acceptance Current

Proportion of current required to charge active material

Faradaic Efficiency

Ratio of acceptance to total current, charge or number of electrons

Self Balancing

When the state of charge of each cell balances out leading to the same charge throughout each cell

Memory Effect

Crystals form reducing the capacity of the battery, occurs when not fully discharged

C-rate

Current at which the battery fully discharges in one hour

Intercalation

When atoms diffuse between sheets of carbon during charge and discharge

Specific charge/discharge capacity

eta= x*F/n*M * 1000/3600 [mAh/g]

Cell Capacity

eta_cell = (eta+)*(eta-)/(eta+)+(eta-)

Cell Voltage

Ecell = Ec - Ea

Power Capacity

eta_w = eta_cell * E_cell

Tafel Equation

j=a*exp(eta/b)

Lead Acid Sulphation

During deep discharge solid and non-conductive PbSo₄ forms on negative electrode leading to irreversible degradation

Lead Acid Trickle Charge

When charging batteries with imbalanced SoC in series, batteries with the highest SoC have a lower faradaic efficiency due to the side reaction of water electrolysis. This allows batteries with a lower SoC to catch up