Voltage, current, electrode of rechargeable battery

Voltage, current, electrode of rechargeable battery

The voltage is the electric field driving force, which is equal to the potential difference between two points in the circuit. Voltage is also called electromotive force, and the unit is volts (V). Since the actual voltage of the battery cell is affected by many conditions, such as temperature and pressure, a reference point is required, that is, the standard state of the electrode (1 bar, 25°C and 1 mol/dm3). The standard electric potential is the measured value of the electric potential in the equilibrium state, which is the basis of the electric potential of each electrode. The actual potential difference between the two electrodes can be expressed as follows:

Erxn = Eright-Eleft (13)
Erxn is a potential difference caused by a chemical reaction, while Eright. and Eleft correspond to the potential of each electrode. For galvanic cells where the redox reaction proceeds spontaneously, Erxn takes a positive value. For electrolytic cells where the redox reaction does not proceed spontaneously, Erxn is a negative value.
When the battery is in a balanced state, there is no or very small current, it can provide the amount of electricity equivalent to △G. Since the current continues to flow inside the battery during the discharge, it can be considered that the battery is in a thermodynamically unbalanced state and cannot generate the maximum possible electrical energy, because the voltage at this time is always less than the open circuit voltage (OCV). The open circuit voltage is the potential difference between the two ends of the device under no applied load. The operating voltage is always lower than the open circuit voltage, which can be explained by ohmic polarization and similar polarization effects caused by charge movement at the electrode/electrolyte interface. On the other hand, the voltage of the reverse charging reaction is higher than the open circuit voltage. The reasons for this phenomenon include internal resistance, overcharge caused by activated polarization, lower ion conductivity than electronic conductivity, impurities in the electrode material, and concentration polarization caused by the difference in the diffusion rate of lithium ions on the surface and inside the electrode, etc. .

Battery charge/discharge voltage and open circuit voltage curve
Battery charge/discharge voltage and open circuit voltage curve

The figure shows the schematic diagram of the voltage change caused by the periodic current pulse during the actual charging and discharging process. The voltage of the charge-discharge curve can be measured by slowly applying current in the standard state, and the graph of the open-circuit voltage can be recorded under the condition of no current passing in the equilibrium state. As mentioned above, the potential difference between the actual voltage and the open circuit voltage measured during the charge and discharge process can be interpreted as the result of polarization.

Current refers to the rate of charge movement, which is closely related to the rate of electrochemical reaction at the electrode. The electrode reaction rate depends on the rate of electron transfer from the electrolyte to the electrode and the surface of the electrode active material.
On the electrode, the reactant O and the product R undergo a reversible electrochemical reaction as shown in formula (14). The relationship between the current and the reaction rate is expressed by the Nernst equation of equation (15) and equation (16).
O+ ne↔R (14)
vf= kfCo(0, t)=ic/nFA(15)
vb =kbCR(0, t)=ia/nFA(16)
In the formula, vf and vb represent the rates of forward and reverse reactions respectively; while kf and kb are the corresponding rate constants; Co and CR are the concentrations of oxides and reductants, respectively, and Co(x, t) is the time t Concentration function of the distance x from the electrode surface; ic and ia represent the cathode and anode currents, respectively; n, F and A represent the number of moles, Faraday’s constant and electrode surface area, respectively.
The net reaction rate is the difference between the forward reaction rate and the reverse reaction rate.
vnet =vf-vb=kfCo(0,t)-kbCR(0,t)=i/nFA (17)
In other words, the current generated by the electrode mainly depends on the net reaction rate. In the equilibrium state, the forward and reverse reaction rates are the same, and the net reaction rate vnet and net current are both 0

Polarization is the phenomenon where the electrode deviates from the equilibrium electrode potential. Since the charge transfer rate of each component of the battery is different, the slowest process is the rate limiting step. When current flows between the two poles of the battery, the actual potential E is always greater than (charging) or less than (discharging) the equilibrium potential Eeq. Overpotential refers to the difference between the actual potential and the equilibrium potential, and it is used to measure the degree of polarization. Actual potential E, equilibrium potential Eeq. The relationship with the overpotential η is expressed as follows:
η=E-Eeq (18)

As shown in the figure, polarization can be divided into ohmic polarization (iR drop), activation polarization and concentration polarization.

The effect of current density on polarization
The effect of current density on polarization

As shown in the figure, the influence of current density on polarization

Here, the iR drop is related to the electrolyte, and has nothing to do with the electrode reaction. Considering that the iR drop increases in proportion to the current density, a sharp drop in the operating voltage under high current density conditions can be avoided by minimizing the internal resistance.
On the other hand, activation polarization is closely related to the characteristics of the electrode. As an inherent property of the active material, it is greatly affected by temperature. Concentration polarization is caused by the concentration gradient of reactants on the surface of the active material. However, it is difficult to distinguish these polarization types in actual batteries.

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