Thermodynamics of Li-Ion Batteries

 Lithium-ion battery, shortly abbreviated as Li-ion battery or LIB is a family of rechargeable battery. Lithium-Ion batteries are now days widely used for the power generation of electric vehicles. The movement of Lithiumions is towards the positive electrode from the negative electrode, during discharge, and from negative to positive electrode when charging. Various chemical and electrochemical reactions take place which is mainly exothermic in nature.

In Lithium-ion electrochemical cells, the electrode material is not the conventional metallic lithium. Instead it is intercalated lithium compound. If proper heat transfer is not done the heat may reside inside the battery itself rather than propagating to the surroundings.                                  ­­

A lithium-ion battery from a laptop computer.

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Cell life of Li-ion

  • When charging forms deposits inside the electrolyte after some period of time, the cell’s capacity diminishes. So internal resistance gets increased and ability to deliver current get decreases. So cell life decreases.
  • The capacity loss gets expedited under elevated temperatures and under High charge levels. This occurs in both ambient air and during charging as well.

Internal resistance of Li-ion

  • Lithium-ion batteries, especially the standard (Cobalt) ones, have a high internal resistance. This rising resistance alleviates battery life and consequently, it stops functioning.
  • It is more efficient to connect in a parallel circuit, a number of small batteries rather than using a single large battery, if the purpose is to power automobiles like electric cars, and other large devices.

Safety requirements

  • LIBs run the risk of being disrupted mainly by cell rupture and due to thermal runaway. This happens when they get overcharged or overheated.
  • This has created an inability to charge many LIBs below temperatures of zero deg C safely
  • Many types of lithium-ion cell cannot be charged safely below 0°C.

Other safety features are required in each cell of Li-ion 

  • Shut-down separator (for overtemperature)
  • Tear-away tab (for internal pressure)
  • Vent (pressure relief)
  • Thermal interrupt (overcurrent/overcharging)

Specifications and design of Li-ion

  • Specific energy density: 150 to 250 W:h/kg
  • Volumetric energy density: 250 to 620 W·h/l
  • Specific power density: 300 to 1500 W/kg

Many fixed and portable devices that normally used Sealed Lead Acid (SLA) and Nickel Metal-hydride (Ni-MH) batteries have started replacing them by Lithium-ion batteries due to their higher energy storage density. Moreover they are lesser in weight and volume as compared to SLA and Ni – MH batteries.

Even though Li-ion batteries are highly efficient to their ancestors, they have certain limitations. Most of the Lithium-Ion (Li-Ion) cells should be avoided charging above 45°C or discharged above 60°C, as they generate heat during charging as well as discharging. This is crucial as an increase in temperatures leads to battery failure due to the process of venting.(David Gunderson, 2009). Hence it has become a great challenge for researchers to design a cell that produces less heat during charging as well as discharging.

The rise in temperature caused by the heat energy in Lithium-ion batteries comes from several sources. Electronic circuit elements around the battery may conduct heat into the cells during its operation.Other sources of heat include protection and gas gauge circuits inside the battery itself, the resistance of nickel strips used to interconnect the cells and circuit board traces etc.As the heat produced is proportional to the square of the current through the element (P = I2 R), for large Li – ion batteries, even the smallest resistive element can produce a considerable amount of heat that may lead to rise in  temperature when charged or discharged for several hours.

Heat generating rates inside the  Li-ion cell is derived from the thermodynamic relations:

Q =    G + T    S + Wal


G = -nFE          S = nFdEeq/dTWel = -nF


                                                     q = I [(Eeq – E) + T dEeq/dT] + qp

Single-phasesolids, multiphase solids and liquid electrolytemixtures contribute to the complexity of LIBs.

Primary electrochemical reactions, mixingand phase changes lead to heat generation

Reliable prediction oftemperature profiles of individual cells, and of a battery system as a whole requires first of allquantitative evaluation of the total heat generation rate.(E. Schuster, H.J. Seifert)

Temperature trends during charging and discharging of Li-ion batteries

During charging of a Lithium ion cell, the chemical reaction that takes place is endothermic and that during discharge is exothermic, which produces heat. This was shown by the study conducted at The Central Research Institute of Electric Power Industry (CRIEPI) in 1995 in a calorimeter.

The diagram below, details the heat flow into and out of the cell during charging and discharging cycle of a single Li-Ion cell. (David Gunderson)

The initial section of the graph marked as “A”, represents the endothermic nature of the charge chemical reaction. The discharge cycle marked “B” is exothermic. The plot shows that near the end of discharge, the heat produced increases rapidly, which indicates a rapid increase in cell impedance near the end of cell capacity when at constant current charge and discharge was used. Thus it can be noted that the endothermic nature of the charge chemical reaction is weak in comparison to other heat sources. This shows that the there was a marked rise in the temperature of the LIBs during charging. This occurred because the endothermic chemical reaction was weak inside the cell causing other heat sources to overpower.

As the discharge nears its end, there are chances of occurrence of a hugerise in temperature due to the exothermic natureof the chemical reaction

Moreover, as the battery voltage decreases near the end of its capacity, the current must increase to maintain constant-power, causing a rise in large battery temperatures and increase in the resistive elements in the battery circuit.

Designing LIBs – Li-ion batteries

There are many factors to consider when designing high current Lithium – ion batteries.

An important criterion while designing LIBs is that there must be a provision to vent out heat that’s gets accumulated inside cells and gets produced from resistive circuit elements. Not only venting, but active cooling provision must also be provided in transportation applications where current levels are more. This is done primarily by use of multiple parallel columns of cells to maintain a constant flow of current. The risk here is that even a single weak cell can cause cell array strapping. So the way to avoid this is to place PTC devices. Although the complexity increases with the use of PTC devices and the costs also go up. (David Gunderson)

Factors such as rates of charge and dischargeand potential-current determine the heat generation rate. Bernadi stated, as per first law of thermodynamicsfor an isobaric battery system, a general energy balance equation for a cell in which the rate of heat generation isgiven by

q = ΣjIj(U ajvg–TU ajvg /T) –  IV +enthalpy-of-mixing term + phase change term    ……(1)

where Ijrefers the volumetric partial reaction current resulting from electrode reaction j,U ajvg   refers the corresponding open-circuit potential (OCP) .

The superscript avg refer tothe value evaluated at the average composition.

I refers the total current in the unit of A/cm3,and V the cell potential.

The first term on the RHS of Eq. 1 represents the enthalpy ofcharge transfer reactions.

The second term stands for the electrical work done by thebattery.

The third term or the enthalpy-of-mixing term represents the heat effectassociated with concentration gradients developed in the cell.

The last term or the phasechange term stands for the heat effect due to phase transformations.

Energy balance was conducted on a thin cell where cell temperature was a constant. Equation 1 helps in calculating heat generation rate in multiple electrode reactions. For a battery system such as lithium-based and nickel-based batteries, the open-circuit potential is a strong function of the local state of charge which is often controlled by solid-state species diffusion.

Non-uniform electrochemical reaction rates occur when species concentration distribution in a cell is not even.

Rao and Newman2 presented a general energy balance equation for insertion battery systems, neglecting enthalpy-of-mixing and phase change terms, in which the rate of heat generation is written as

q = -1/VcVcΣjasjinj(Uj–TUi /T)dv –  IV     …..(2)

where asj is the specific surface area active for electrode reaction j, inj the transfer currentdensity due to reaction j, and Uj the local open-circuit potential of reaction j.

De Vidts et alpresented a similar expression for heat generation rate for a nickel-hydrogen cell,with the pressure work additionally taken into account. Unlike Eq. 1, Equation 2 relatesthe heat generation to the local electrochemical reaction ratesand the local open-circuit potentials. This thus helps in working out the heat generation rate in dynamic conditions and relaxed states.

The part of the cell with highest temperature is responsible for activating thermal runaway. This is why it is crucial to know the temperature distribution pattern in the cell.

Based on the overall heat balance of a cell, both Eqs. 1and 2 become inadequate when the temperature profile inside a cell is to be found out.

Maxwell’s relations(general) 

If Φ is a thermodynamic potential and xi and xj are two different natural variables for that potential, then the Maxwell relation for that potential and those variables is:

The four most common Maxwell relations are the equalities of the second derivatives of each of the four thermodynamic potentials, with respect to their thermal natural variable (temperature T; or entropy S) and their mechanical natural variable (pressure P; or volume V):

 Maxwell’s relations(common)


The oxide family with the general formula Li1+x(NiyMnzCo1-y-z)1-xO2, called NMC, is believed to be one of the most promising substitute of the current industrial standard.The NMC compounds are layered oxides, with the same crystallographic structure of theLiCoO2. The most studied NMC compounds are the ones with z = y. x is called the overlithiation degree. It indicates the excess of lithium in the structure of the NMC compounds. The lithium ion excess is located in the layers of the transition metals (slab).


M + e- = M+ + 2e-

Where M indicates the gaseous molecule.

If the energy of the electron beam is very high, themolecule can be fragmented, due to the instability of the ion produced:

M+ = m1+ + m2

Where m1 and m2 are two fragments of the molecule M. It also happens that in the ionizationprocess two fragments with opposite charge are formed:

M + e- = m1+ + m2- + e-


LIBs are used widely in devices and electronic equipment, automobiles, aeronautical equipment, military devices etc. They are popular, portable and have good energy densities. Further added to their benefits are slow losses of charge when not in use and no memory effect.


  1. Bernardi, E. Pawlikowski, and J. Newman, “A General Energy Balance for Battery Systems,

” J. Electrochem. Soc., 132, 5 (1985).

  1. Rao and Newman, “Heat Generation Rate and General energy Balance forInsertion Battery
    systems,” J. Electrochem. Soc., 144, 2697 (1997).
  2. De Vidts, J. Delgado, B. Wu, D. See, K. Kosanovicb, and R.E. White, “A Nonisothermal Nickel-
    Hydrogen Cell Model,” J. Electrochem. Soc., 145, 3874 (1998).

David Gunderson, Li-ion Battery Temperature Trends During Charge and Discharge, Retrieved from http://www.micro-power.com/userfiles/file/mp_tempcharge-1250026530.pdf. Retrieved on 02 May 2012

David Gunderson, 2009, Keep An Eye On Temperature Trends During Li-ion Battery Charge And Discharge Cycles, Retrieved from http://electronicdesign.com/article/power/keep-an-eye-on-temperature-trends-during-li-ion-ba. Retrieved on 02 May 2012

Thermodynamics of Lithium Intercalation into Graphites and Disordered Carbons Y. F.Reynier, R. Yazami,a and B. Fultz*,z Journal of The Electrochemical Society, 151 ~3! A422-A426 2004! – pdf

Elke Schuster, The thermodynamics of Lithium. Retrieved from www.spp1473.kit.edu/…/Elke_Schuster_The_Thermodynamics_of_Lithium ion batteries/. Retrieved on 02 May 2012.

Noboru Sato, Thermal behavior analysis of lithium-ion batteries for electric and hybrid vehicles, Retrieved from www.sciencedirect.com/science/article/pii/S0378775301004785. Retrieved on 02 May 2012.

ThermodynamicsModeling and Simulating of Lithium-Ion Battery Pack under Electric Vehicle
Driving Cycle – LUOYutao, TAN Di, HEXiaochan – (Schoolof Mechanical and Automotive Engineering, South  China University of Technology,Guangzhou510640, China)

The limits of energy storagetechnology-Bulletin of the Atomic Scientists- Retrieved from www.thebulletin.org/web-edition/columnists/kurt-zenz-house/the-limits-of-energy-storage-technology. Retrieved on 02 May 2012.

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