The basic principle of a rechargeable battery is the conversion of chemical energy to electrical energy during the discharge process and vice versa during the charge process. The pertinent electrochemical reactions responsible for the energy conversion occur at the site of the electrode- electrolyte interface. The electrolyte acts as a filter for the passage of Li+ ions between the electrodes, but does not allow the flow of electrons. During the discharge process, i.e when the electrical energy is utilized by connecting the battery terminals to an external load, oxidization reaction occurs at the anode wherein electrons are generated. These electrons travel through the external circuit, pass through the load and arrive at the cathode where they are consumed for the reduction reaction. Hence, the anode is termed as the negative electrode and cathode is termed as the positive electrode. The Li+ ions also travel from anode to cathode inside the battery to balance the charge. During the charging process, the load in the external circuit is replaced with a power supply where the electrons are drawn from the cathode and driven across the external
circuit to the anode. The anode takes the electrons where the reduction reaction converts the electrical energy to chemical energy, which is again available during the next discharge process.
When the external circuit is open or when no current is drawn from the cell, the electrostatic driving force in the opposite direction balances the chemical driving force on the mobile Li+ species in one direction. The chemical driving force, which is the difference in the chemical potentials of the anode and cathode, is expressed using the standard Gibbs free energy change per mole of reaction represented as ∆Gr°.
c a r
G
The equivalent available electrostatic free energy per mole is given by –nFE°, where n represents the number of electrons of charged species transferred by per mole of reactants and E° represents the standard electrical potential difference between the two electrodes in equilibrium.
nFE Gr nF E nFE c a c a
Hence, it is apparent to increase the battery’s overall capacity and cell voltage in order to obtain higher energy densities. As mentioned in the previous section, the overall cell voltage depends on the intrinsic material properties (chemical potential, μLi) of the anode and cathode. However, it is also essential that the materials chosen be such that difference in the chemical potentials does not adversely affect the electrochemical stability of the electrolyte. Figure 3 shows the Fermi energy levels of the anode, cathode and electrolyte, respectively [37]. The Fermi energy level of the cathode (Ec) should be above the highest occupied molecular orbitals
level of the anode should be below the lowest unoccupied molecular orbitals (LUMO) of the electrolyte to prevent any reduction reaction due to anode. In summary, it is extremely important that the anode and cathode materials be selected or designed such that the difference in redox energies (Ea-Ec or eVoc) lie within the band gap (Eg) of the electrolyte thereby indicative of a
stable electrochemical system.
Figure 3: Schematic illustration of relative energies of electrolyte energy gap and the electrodes
E° is also expressed as the open circuit voltage Eoc at thermodynamic equilibrium when
no current passes through the electrochemical cell. However, during practical operations, the resistance of the electrolyte to ionic transport at the electrode-electrolyte interfaces and electrical resistance between the individual cell components give rise to cell impedance. The internal resistance of the electrochemical cell is given by the following equation:
e el R R R R int A L R i el
Where Rel represents the electrolyte resistance, Rint is the interfacial resistance at the
electrode-electrolyte interface for the charge transfer reactions and Re represents the sum of
internal contact resistances arising from all the individual cell components. This resistance arising from the electrolyte (Rel) is governed by the thickness of the separator (L) or the effective
distance between the anode and cathode, the ionic conductivity of the electrolyte (σi) and the
effective area between the electrodes (A). Therefore, when a load is applied or current is drawn from a battery, there is a drop in the open circuit potential due to the internal impedances/resistance, which is given by the following equation:
IR E E oc
The difference in the thermodynamic equilibrium voltage and the output voltage as a function of current is also known as polarization and the voltage-current characteristic curve is termed as polarization curve. Figure 4 shows a typical polarization curve during the discharge process. The shape of the curve is determined by the kinetic limitations of the reactions and other processes that occur during the battery operation. The slope of the curve varies according to the current applied and can be divided into three distinct regions as shown in the Figure 4.
In region-I, there is a rapid decrease in voltage with current and is referred to as activation polarization wherein, the impedances are due to the kinetics involved with the charge- transfer reactions that occur at the electrode-electrolyte interface of the cathode and anode. Following region-I, there is a slight change in voltage in region-II which is known as ohmic polarization. This region encompasses all the resistances: electrolyte resistance, resistance due to current collectors and other cell components, resistance between the active materials present in the electrode, and the resistance between the current collector foil and the electrode coating. Following this region, there is a rapid decrease in voltage known as concentration polarization as shown in the region-III. The electroactive species at the electrode-electrolyte interface is continuously consumed by the discharge reaction process and needs to be replenished from the bulk. At higher current densities, the limitations due to diffusion of species become more prominent and hence require an electrolyte with high ionic conductivity to transport the ions to the interface more rapidly in order to sustain the charge-transfer reactions. Electrode materials with improved electronic conductivity could also aid this process thereby facilitating the transport of electrons and ions thus leading to lower charge transfer resistances.