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In the charge-discharge testing or actual use of lithium-ion batteries, the voltage parameters mainly include plateau voltage, median voltage, average voltage, cut-off voltage, etc. The typical discharge curve is shown in Figure 1.

The plateau voltage refers to the voltage value corresponding to the situation where the voltage change is minimal while the capacity change is relatively large. Lithium iron phosphate and lithium titanate batteries have obvious plateau voltages, and the voltage plateau can be clearly identified in the charge-discharge curves. For most batteries, the voltage plateau is not obvious. During charge-discharge testing, data is collected at voltage intervals, and then the voltage curve is differentiated. The plateau voltage is determined by the peak value of dQ/dV.

The median voltage is the voltage value corresponding to half of the battery capacity. For materials with an obvious plateau, such as lithium iron phosphate and lithium titanate, the median voltage is generally the plateau voltage.

The average voltage is the effective area of the voltage-capacity curve (i.e., the battery charge/discharge energy) divided by the capacity. The calculation formula is Ü = ∫U(t)*I(t)dt / ∫I(t)dt. In the charge-discharge test data, the average voltage is obtained by dividing the charge or discharge energy by the capacity data. Conversely, the energy density of the battery is also estimated based on the average voltage of the battery, that is, energy = capacity * average voltage / battery mass (or volume).

The cut-off voltage refers to the lowest voltage allowed when the battery is discharging and the highest voltage allowed when the battery is charging. If the battery continues to discharge after the voltage drops below the discharge cut-off voltage, the potential of the positive electrode of the battery will continuously decrease, while the potential of the negative electrode will rise rapidly, resulting in over-discharge. Over-discharge may cause damage to the active materials of the electrodes, lose their reaction ability, and shorten the battery life. It will also cause the decomposition of the negative electrode copper foil and precipitation on the positive electrode, posing a risk of short circuit. If the charging voltage is higher than the charging cut-off voltage, the potential of the positive electrode of the battery will continuously increase, causing excessive delithiation of the positive electrode material, destruction of the crystal structure and failure, and decomposition of the electrolyte and loss of lithium ions. Meanwhile, the potential of the negative electrode will continuously decrease, with excessive lithiation, collapse of the graphite layered structure, and lithium precipitation on the electrode surface.

In fact, the voltage U(battery) of the battery is determined by the difference between the electrode potential E(positive electrode) and the electrode potential E(negative electrode) of the positive electrode, as represented by Equation (1):

U(battery) = E(positive electrode) - E(negative electrode) Equation (1)

In the battery system, the standard lithium electrode is commonly used as a reference electrode. The electrode potentials of the positive and negative electrode materials are generally the potentials generated by the reactions between the reactants and products and the reference lithium electrode. As shown in Figure 2, during the charge-discharge process, the positive and negative electrode materials undergo delithiation or lithiation, and the electrode potentials change. The battery voltage is the difference between the two.
Therefore, to understand the voltage of the battery, it is first necessary to understand the electrode potentials of various electrode materials. Understanding the equilibrium electrode potential curves of materials can better understand the voltage characteristics of the battery.

The open-circuit voltage refers to the potential difference between the positive and negative electrodes of the battery when it is in a non-working state, that is, when no current flows in the circuit. When the electrode material is assembled with metallic lithium into a button half-cell, the open-circuit voltage is the equilibrium potential of the electrode material.

Open-Circuit Voltage Testing Methods
The process of testing the equilibrium potential of the electrode material is as follows: The electrode material is prepared into an electrode sheet, assembled with metallic lithium into a button half-cell, the open-circuit voltage of the button half-cell under different SOC states is measured, and a mathematical expression of the open-circuit voltage curve is determined by using polynomial or Gaussian fitting, etc. The open-circuit voltage testing methods mainly include:

1. Galvanostatic Intermittent Titration Technique (GITT): The basic principle is to apply a constant current to the measurement system in a specific environment for a certain period of time and then cut off the current. Observe the change of the potential of the system with time during the current application period and the voltage that reaches equilibrium after relaxation (i.e., the open-circuit voltage). An example of GITT testing is as follows: (i) Charge at C/50 until the voltage reaches the upper limit voltage, such as 4.2 V; (ii) Stand still for 2 hours; (iii) Discharge at 1C for 6 minutes and record the discharge capacity; (iv) Stand still for 15 minutes and record the voltage; (v) Repeat steps (iii) and (iv) a total of 9 times; (vi) Discharge at C/50 until the voltage reaches the lower limit voltage, such as 3.0 V; (vii) Normalize the capacity-voltage curve recorded in steps (iii) and (iv), make it into an SOC-voltage curve, and fit to obtain the mathematical expression of the open-circuit voltage curve.

2. Low-current Charge-Discharge Curve: Charge and discharge with a constant current at a particularly low rate (such as 0.01C), set the upper and lower limits of the voltage range, obtain the battery's low-current charge-discharge curve, take the points with the same charge amount as the starting point of the curve, take the average of the voltages in the charge-discharge curve, normalize the abscissa of the curve according to the theoretical capacity, and then use curve fitting to obtain the open-circuit voltage curve.

Battery Polarization
The phenomenon that the electrode deviates from the equilibrium electrode potential when current passes through the electrode is called battery polarization, and polarization generates overpotential. According to the causes of polarization, polarization can be divided into ohmic polarization, concentration polarization, and electrochemical polarization.

Ohmic Polarization: It is caused by the resistance of each part of the battery connection. The voltage drop value follows Ohm's law. When the current decreases, the polarization immediately decreases, and it disappears immediately after the current stops.

Electrochemical Polarization: It is caused by the slowness of the electrochemical reaction on the electrode surface. It significantly decreases within microseconds as the current becomes smaller.

Concentration Polarization: Due to the slowness of the ion diffusion process in the solution, a concentration difference between the electrode surface and the solution bulk is caused under a certain current, resulting in polarization. This polarization decreases or disappears on a macroscopic second level (from several seconds to tens of seconds) as the current drops.

The internal resistance of the battery increases with the increase of the battery's discharge current. This is mainly because a large discharge current increases the polarization trend of the battery, and the larger the discharge current, the more obvious the polarization trend, as shown in Figure 2. According to Ohm's law: V = E0 - I×RT, with the increase of the overall internal resistance RT, the time required for the battery voltage to reach the discharge cut-off voltage is correspondingly reduced, so the discharged capacity is also reduced.

Lithium-ion batteries are essentially lithium-ion concentration difference batteries. The charge-discharge process of lithium-ion batteries is the process of lithium-ion insertion and extraction in the positive and negative electrodes. The factors affecting the polarization of lithium-ion batteries include:

2.1 Influence of the Electrolyte: The low conductivity of the electrolyte is the main reason for the occurrence of polarization in lithium-ion batteries. In the general temperature range, the conductivity of the electrolyte used in lithium-ion batteries is generally only 0.01～0.1S/cm, which is one percent of that of aqueous solutions. Therefore, when lithium-ion batteries are discharged at a large current, there is not enough time to supplement Li+ from the electrolyte, and polarization will occur. Improving the conductivity of the electrolyte is a key factor in enhancing the large-current discharge ability of lithium-ion batteries.

2.2 Influence of the Positive and Negative Electrode Materials: If the particles of the positive and negative electrode materials are large, the channels for lithium ions to diffuse to the surface are lengthened, which is not conducive to high-rate discharge.

2.3 Conductive Agent: The content of the conductive agent is an important factor affecting the high-rate discharge performance. If the content of the conductive agent in the positive electrode formula is insufficient, when discharging at a large current, electrons cannot be transferred in a timely manner, the polarization internal resistance increases rapidly, and the battery voltage quickly drops to the discharge cut-off voltage.

2.4 Influence of the Electrode Sheet Design:

Electrode Sheet Thickness: In the case of large-current discharge, the reaction speed of the active materials is very fast, requiring lithium ions to be quickly inserted and extracted in the materials. If the electrode sheet is relatively thick, the diffusion path of lithium ions is increased, and a large lithium-ion concentration gradient will be generated in the thickness direction of the electrode sheet.

Compacted Density: If the compacted density of the electrode sheet is relatively large, the pores become smaller, and the movement path of lithium ions in the thickness direction of the electrode sheet is longer. In addition, if the compacted density is too large, the contact area between the material and the electrolyte is reduced, the electrode reaction sites are reduced, and the battery internal resistance is also increased.

2.5 Influence of the SEI Film: The formation of the SEI film increases the resistance of the electrode/electrolyte interface, resulting in voltage hysteresis, that is, polarization.

The Working Voltage of the Battery
The working voltage, also known as the terminal voltage, refers to the potential difference between the positive and negative electrodes of the battery when it is in a working state, that is, when current flows in the circuit. When the battery is in a discharging working state, when current flows through the inside of the battery, it is necessary to overcome the resistance caused by the internal resistance of the battery, which will cause ohmic voltage drop and electrode polarization. Therefore, the working voltage is always lower than the open-circuit voltage. When charging, it is the opposite, and the terminal voltage is always higher than the open-circuit voltage. That is, the result of polarization makes the terminal voltage lower than the electromotive force of the battery when the battery is discharging, and when the battery is charging, the terminal voltage is higher than the electromotive force of the battery.

Due to the existence of the polarization phenomenon, there will be a certain deviation between the instantaneous voltage and the actual voltage during the charge-discharge process of the battery. When charging, the instantaneous voltage is slightly higher than the actual voltage, and after the charging is completed, the polarization disappears and the voltage drops back. When discharging, the instantaneous voltage is slightly lower than the actual voltage, and after the discharging is completed, the polarization disappears and the voltage rises back.

Combined with the above, the composition of the battery terminal voltage is shown in Figure 3, and the expressions are:

Charging: VCH = （E+ - E-）+ VR =（E+0+η+）- （E-0 - η-）+ VR

Discharging: VD = （E+ - E-）- VR =（E+0-η+）- （E-0 + η-）- VR

Why do some materials have obvious voltage platforms while others do not?

In thermodynamics, the degree of freedom F is the factor (such as temperature and pressure) that can be independently changed without changing the number of phase states when the system is in an equilibrium state. The number of these variables is called the degree of freedom. The relationship between the degree of freedom of the system and other variables:

F = C - P + n

Where F: represents the degree of freedom of the system; C: the number of independent components of the system; P: the number of phase states; n: external factors, usually taking n = 2, representing pressure and temperature.

For the lithium-ion electrochemical system, the external factors n = 2, taking voltage and temperature respectively. Assume that the temperature and pressure of the lithium-ion electrode materials remain constant during the charge-discharge process. Here, we discuss the binary system (C = 2). If there is one phase in a particle, that is, P = 1, then F = 1, and the chemical potential is a degree of freedom that changes with the change of lithium concentration (for example, lithium cobaltate in solid solution, one phase, and the lithium concentration is constantly changing).

If there are two phases in the particle, that is, P = 2, then F = 0. When two phases coexist, there is a flat voltage platform in a binary system electrode material (for example, lithium iron phosphate, two phases coexist, and the lithium concentration in each phase is constant).

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