What are the main electrode reactions in a lithium battery?
Electrode processes in a battery generally include ion transport in the solution phase, ion transport within the electrode, electron conduction within the electrode, charge transfer, charging and discharging of the electric double layer or space charge layer, adsorption and desorption of cations and anions in the solvent and electrolyte, adsorption and desorption of gaseous reactants or products, nucleation and growth of new phases, chemical reactions coupled with electrochemical reactions, volume changes, and endothermic and exothermic processes. Some of these processes occur simultaneously, while others occur sequentially.
The driving forces of the electrode process include electrochemical potential, chemical potential, concentration gradient, electric field gradient, and temperature gradient.
Distinguish between two-electrode and three-electrode electrodes.
Electrochemical measurements generally use two-electrode or three-electrode cells, and four-electrode cells are rarely used.
Two electrodes
The two electrodes consist of a working electrode (W) and a counter electrode (C). Most lithium battery research focuses on two-electrode batteries. The voltage measured in a two-electrode battery is the difference between the positive and negative electrode potentials, and it is not possible to obtain the potential of either the positive or negative electrode and its electrode process kinetics information in isolation.
Three electrodes
A three-electrode battery consists of a working electrode (W) and a counter electrode (C), respectively, and a reference electrode (R). Polarization of the electrodes is achieved through a polarization current between W and C. A very small current is passed between W and R to measure the potential of the working electrode.
A three-electrode cell allows for the specialized study of electrode process kinetics at the working electrode.
Characteristics of the reference electrode
1. The reference electrode should be a reversible electrode:
2. It is not easily polarized, thus ensuring that the electrode potential comparison is standardized and constant:
3. It has good recovery characteristics and does not exhibit severe hysteresis;
4. It exhibits good stability and reproducibility;
5. During rapid transient measurements, the reference electrode is required to have low resistance to reduce interference and improve the stability of the measurement system;
6. For different solution systems using the same reference electrode, the measurement results may differ. The error mainly comes from the mutual contamination between solution systems and the difference in liquid junction potential.
Commonly used reference electrodes
Reference electrodes for aqueous solution systems include: reversible hydrogen electrode, calomel electrode, mercury-mercury oxide electrode, and mercury-mercurous sulfate electrode.
Reference electrodes for non-aqueous systems: silver-silver chloride electrode, Pt electrode, and electrodes made of metallic lithium, sodium, etc.
Other options include using silver or platinum wires as quasi-reference electrodes, or using ferrocene redox couples that are electrochemically stable and dissolved in the electrolyte.
For details on quasi-reference electrodes, please refer to AJ Bard's book (Electrochemical Methods).
Electrode process
Electrode processes generally include the following basic processes or steps:
1. Electrochemical reaction process: The process of gaining or losing electrons to generate reaction products at the electrode/solution interface, i.e., the charge transfer process;
2. Mass transfer process: The process by which reactants are transferred to the electrode surface or interior, or reaction products are transferred from the interior or surface of the electrode into the solution or back into the electrode (diffusion and migration);
3. The charging and discharging process of the double layer near the electrolyte and the space charge layer near the inner electrode at the electrode interface;
4. Electromigration of ions in solution or conduction of electrons within an electrode.
In addition, along with electrochemical reactions, there are also adsorption/desorption processes of solvents, cations and anions, and electrochemical reaction products, new phase growth processes, and other chemical reactions.
Typical electrode processes and kinetic parameters
Ion migration resistance in electrolytes (Rsol); ion adsorption resistance and capacitance on electrode surfaces (Rad, Cad); electrochemical double layer capacitance (Cdl); space charge layer capacitance (Csc); ion transport resistance at the electrode-electrolyte interface (Rincorporation); ion transport resistance and capacitance in surface films (Rfilm, Cfilm); charge transfer (Rct); ion diffusion resistance in electrolytes (Zdiffusion); ion diffusion in electrodes (Zdiffusion) – bulk diffusion (Rb) and diffusion at grain boundaries (Rgb); storage capacitance of foreign atoms/ions in the host lattice (Cchem); phase transition reaction capacitance (Cchem); electron transport (Re).
It is worth noting that the response time of different electrode processes is different. In general, the order is: charge transfer < surface reaction < electron transport < interfacial diffusion < solid-phase reaction < bulk diffusion. Therefore, the diffusion of ions inside the electrode and electrolyte materials and the solid-phase reaction are generally rate-controlled steps.
Polarization and Types
When an external electric field is applied, the battery or electrode gradually deviates from its equilibrium potential; this is called polarization. The difference between the polarization potential and the equilibrium potential is called the overpotential.
In batteries without a mobile phase, there are three types of polarization:
1. Chemical polarization – Polarization related to charge transfer processes, driven by the electric field gradient. The magnitude of electrochemical polarization is determined by the electrochemical reaction rate, and the magnitude of the electrochemical polarization resistance (Rct) is directly related to the exchange current density.
2. Concentration polarization – polarization related to the diffusion process of reactants and products involved in electrochemical reactions, driven by the concentration gradient. Concentration polarization is related to the diffusion coefficient of mass transfer particles.
3. Ohmic polarization – polarization related to the transport of charge carriers in each phase of the battery, driven by the electric field gradient. The magnitude of ohmic polarization is determined by the sum of various resistances involved in electromigration within the battery, i.e., ohmic resistance.
If other basic electrode processes exist, such as homogeneous or heterogeneous chemical reaction processes, then chemical reaction polarization may occur.
Classic Applications of Electrochemical Measurement Methods in Lithium Batteries
Lithium-ion battery electrode materials generally undergo the following steps during battery charging and discharging:
1. Formed lithium ions migrate from the electrolyte to the electrolyte/solid electrode interface;
2. Solventized lithium ions are adsorbed at the interface between the electrolyte and the solid electrode;
3. Desolvation;
4. Charge transfer: Electrons are injected into the conduction band of the electrode material, and adsorbed lithium ions migrate from the electrolyte phase to the surface lattice of the active material;
5. Lithium ions diffuse or migrate from the surface lattice of the active material into its interior;
6. Electron migration from the current collector to the active material.
Cyclic voltammetry
It is commonly used to investigate the reversibility of electrode reactions, electrode reaction mechanisms (such as intermediates, phase boundary adsorption/desorption, new phase formation, properties of coupled chemical reactions, etc.), and electrode reaction kinetic parameters (such as diffusion coefficient, electrode reaction rate constant, etc.).
When the potential is scanned towards the cathode, the electroactive material is reduced at the electrode, producing a reduction peak; when scanned towards the anode, the reduction product is re-oxidized at the electrode, producing an oxidation peak. Therefore, one scan completes one cycle of reduction and oxidation, and the current-voltage curve of this cycle is called the cyclic voltammetry curve.
By analyzing the peak heights, symmetry, distance between the oxidation and reduction peaks, and midpoint of the cyclic voltammetry curves, the reversibility and polarization of the electroactive material's reaction on the electrode surface can be determined. If the overpotential difference between the oxidation and reduction reactions is not significant, the midpoint value between a pair of oxidation and reduction peaks can be approximated as the thermodynamic equilibrium potential of the reaction.
Furthermore, by differentiating the voltage-capacity curve of constant current charging and discharging and using dQ/dV as the vertical axis and voltage as the horizontal axis, a result very similar to the CV curve can be obtained, and in essence, there is no difference.
Calculation of lithium-ion diffusion coefficient by cyclic voltammetry
Note: This only applies when the diffusion process is the controlling step and the electrode is a reversible system, in which case the formula is given.
At room temperature,
In the formula, Ip is the peak current, n is the number of electrons participating in the reaction, A is the electrode area immersed in the solution, F is the Faraday constant, DLi is the diffusion coefficient of Li in the electrode, v is the scan rate, and ΔC0 is the change in the concentration of the target substance before and after the reaction.
The calculation can be performed using the following steps:
1. Measure the cyclic voltammetry curves of the electrode material at different scan rates;
2. Plot the peak current at different scan rates against the square root of the scan rate;
3. Integrate the peak current and measure the change in lithium concentration in the sample;
4. Substitute the relevant parameters into equation (2) to obtain the diffusion coefficient.
It should be noted that, for the following reasons, the absolute values obtained vary in different literature.
This reaction requires diffusion control, and the chemical diffusion coefficient measured by cyclic voltammetry is not the intrinsic ion diffusion coefficient within the electrode material (see extended reading for details). Furthermore, if it is a porous powder electrode, its actual reaction area is much larger than the electrode's geometric area, and it is difficult to measure accurately, introducing significant uncertainty into the results.
Of course, we will explain the principles and applications of the cyclic voltammetry method in detail elsewhere.
Constant current intermittent titration technique
The galvanostatic intermittent titration technique was proposed by German scientist W. Weppner. The basic principle is to apply a constant current to the measurement system under a specific environment and continue it for a period of time before cutting off the current. The change of the system potential over time during the current application period and the voltage at which equilibrium is reached after relaxation can be observed. By analyzing the change of potential over time, the relaxation information of the electrode process overpotential can be obtained, and then the reaction kinetic information can be inferred and calculated.
The lithium-ion diffusion coefficient can be calculated when the system meets the following conditions.
1. The electrode system is an isothermal adiabatic system;
2. The electrode system exhibits no volume change or phase transition when an electric current is applied;
3. The electrode response is entirely controlled by the diffusion of ions within the electrode;
4. τ≤L²/D, where L is the ion diffusion length;
5. The electronic conductivity of the electrode material is much greater than its ionic conductivity, etc.
The calculation formula is as follows:
In the formula, DLi is the chemical diffusion coefficient in the electrode, Vm is the volume of the active material, A is the actual electrode area immersed in the solution, F is the Faraday constant, n is the number of electrons participating in the reaction, I0 is the titration current value, dE/dx is the slope of the open circuit potential versus Li concentration curve at a certain concentration (i.e., the coulometric titration curve), and dE/dt1/2 is the slope of the polarization voltage versus the square root of time curve.
The basic process for measuring the lithium chemical diffusion coefficient in electrode materials using the GITT method is as follows: At a certain moment during the battery charging and discharging process, a small current is applied and kept constant for a period of time before being cut off; the change of electrode potential over time after the current is cut off is recorded; a polarization voltage versus time square root curve, i.e., the dE/dt1/2 curve, is plotted; the coulometric titration curve, i.e., the dE/dx curve, is measured; and the diffusion coefficient is solved using the formula by substituting the relevant parameters.
Constant potential intermittent titration technique
Potentiostatic intermittent titration (PITT) is a measurement method that involves instantaneously changing and maintaining a constant electrode potential while simultaneously recording the change in current over time. By analyzing the change in current over time, information about the electrode process potential relaxation and other kinetic information can be obtained. It is similar to a constant potential step titration, except that PITT is a multi-potential point measurement.
The formula for measuring the chemical diffusion coefficient of lithium ions using potentiostatic intermittent titration is as follows:
In the formula, i is the current value, t is the time, ΔQ is the charge embedded in the electrode, DLi is the diffusion coefficient of Li in the electrode, and d is the thickness of the active material.
The basic operation is as follows: change the electrode potential instantaneously with a constant potential step and record the change of current over time; use the ln(i)-t curve; extract the data of the linear part of the ln(i)-t curve and calculate the slope to obtain the lithium-ion chemical diffusion coefficient.
Potential relaxation technique
The potential relax technique studies the change of electrode potential over time under conditions where there is no exchange of matter or energy between the battery and its external environment. This method belongs to the current interruption method within current step measurement methods, and is consistent with the GITT experimental method, except that it analyzes the potential change during the relaxation process. This method was first applied by Wang Qing et al. from the Institute of Physics, Chinese Academy of Sciences, to the study of ion diffusion kinetics in lithium-ion battery electrode materials.
The calculation formula is:
In the formula, ψm is the equilibrium electrode potential, ψ is the initial potential, R is the gas constant, T is the absolute temperature, d is the thickness of the active material, DLi is the diffusion coefficient of Li in the electrode, and t is the time when the potential reaches equilibrium.
The specific measurement steps are as follows: pre-charge and discharge the battery to reduce its coulombic efficiency to about 97%; when the battery is charged/discharged to a certain extent, cut off the current and use CPT (chrono potentiometry technique) to record the voltage change curve over time; plot ln[exp(ψm-ψ)xF/RT-1]-t using the formula, and perform linear fitting on the latter half; fit the ln[exp(ψm-ψ)xF/RT-1]-t curve, solve for the slope of the fitted curve, and use the formula to obtain the chemical diffusion coefficient of lithium.
Measuring electrode process kinetics using potential relaxation techniques requires certain preconditions. Typically, lithium-ion batteries undergo several charge-discharge cycles during the first cycle, with the formation of the SEI film being a typical example. To avoid interference from these side reactions on the measurement of the lithium-ion chemical diffusion coefficient, the battery usually needs to complete several charge-discharge cycles before the chemical diffusion coefficient can be measured. Furthermore, since potential relaxation is a very slow process, generally taking around 8 hours, if the potential still cannot reach equilibrium after a long relaxation period, it may be due to instrument leakage, requiring special attention.
