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  Battery Impedance Measure Principle(Understanding measuring circuit and equiv.....


What is the Current Flow in a battery? 


The flow of electricity in electric and electronic devices and the flow of electricity in electrochemistry are largely different as follows. The flow of electricity in electrical and electronic devices is mainly the flow of current in resistors, capacitors, inductors, and semiconductors. This is due to the conduction band of the metal, the donor moves through the space of the acceptor, the electric field in the capacitor, and the back-EMF in the inductor due to some energy converted into the magnetic field energy. However, (Household appliances). However, in electrochemistry, electrons and charges move through the conduction band of the metal, but electricity flows through the energy exchange or phase change at the electrolyte solution and interface. In electrochemistry, the potential is considered based on the movement of electrons, and oxidation and reduction reactions are observed. 
In short
In electrical and electronic devices
1. conductor, inductor Electron transfer through Conduction Band
2. Semiconductors Donor moves through the space of the acceptor
3. Capacitors Movement of electric field (Characteristics of supercapacitors are different from those of electric and electronic devices.) Supercapacitors are electrochemical cells, and capacitors in electric and electronic devices are electric energy storage.)

In electrochemical reactions
1. Electric conduction Electron transfer through conduction band
2. Electrolyte solution ion
3. Electrode, electrolyte solution interface oxidation-reduction reaction charge accumulation
Electrolyte solution / electrode interface

The interface in electrochemistry can be diagrammed as below. At the interface, a potential difference occurs according to the density of the electrode electrons. When the potential difference is changed based on LUMO and HOMO, it is involved in the ion and oxidation and reduction reactions.
In order for the potential to change based on the range of LUMO and HOMO, the density of electrons and charges must be increased or decreased, and oxidation and reduction reactions do not occur until this time.
The current flowing up to the time until the oxidation and reduction reactions occur when electrons are accumulated is called a non-faradic current. The characteristics of the current flow are the same as those of a capacitor. This is denoted by Cdl (Double-layer Capacitance).
If change until to potential that can be occur oxidation-reduction reactions, oxidation and reduction occur. The current flowing at this time is referred to as Faradaic Current, and the characteristic of this current has a characteristic of resistance. This is denoted by Rct (Charge Transfer Resistance).

• Double-Layer Capacitance (Cdl) : When an electric charge is applied to the electrode, charges are accumulated on the surface of the electrode.
• Charge Transfer Resistance (Rct) : When the charge storage capacity is exceeded, the electrode reaction proceeds. 

Electrode Reaction Path - Surface(Double Layer) Reaction

The above-described reaction in the electrode can be interpreted as an electrically equivalent circuit as an example of a lithium ion battery as follows.
Rct (Charge Transfer Resistance) and Cdl (Double-layer Capacitance) at the interface of the electrode surface (Double Layer) are formed in parallel. 


Representation of electrode / electrolyte interface : Randles

The resistance Rsol for the electric current in the electrolyte solution is added to the circuit composed of Rct and Cdl in the interface (Double Layer) in series.
The final equivalent circuit is completed by adding the resistance Zw by the diffusion of the electrolyte here.

The interface can not represent R and C in series.
It is because infinity resistance comes out from C.

Reasons for using impedance spectroscopy to analyze circuits in electrochemical cells

The method of analyzing the electrochemical cell is classified into four major categories as follows

Constant Voltage (PotentioStat Mode)
=> To maintain the constant voltage, change the current according to the resistance of the sample (time-dependent) / capacitance (time-dependent).
=> Apply constant voltage and measure current
Constant Current (GalvanoStat Mode)
=> To maintain the constant current, change the voltage according to the resistance of the sample (time-dependent) / capacitance (time-dependent).
=> Apply a constant current and measure the voltage
Equilibrium state voltage(Open Circuit Voltage, Potential Analysis), open circuit between electrodes, closed loop
=> Measuring voltage in a state where no current flows(equilibrium state) in the electrochemical cell 
Impedance spectroscopy (Electrochemical Impedance Spectroscopy)
=> Sine Wave with Amplitude below Non-Faraday Potential where Oxidation and Reduction Does Not Occur Applied Response to Amplitude Change and Phase Change by Frequency.
Equivalent circuit and parameter analysis using Nyquist Plot method.

Therefore, we analyze the cell using the above four methods appropriately.
This lecture deals with the analysis method of analysis using impedance spectroscopy.

Magnitude in equivalent circuit of electrochemical cell & phase


It can be seen that the magnitude and phase of the response current vary with the applied voltage as the frequency changes.
The Nyquist Plot is shown below. In other words, Magnitude and Phase change of the response signal to the applied signal according to the frequency change can be seen at a glance through the Nyquist Plot. This makes it easy to guess the circuit's construction (see the Impedance Spectroscopy Principles section on this menu for more details on this part).

Chemical Equivalent Circuit


Electrode area and reactance at the same frequency

At the same frequency, there is a change in reactance (capacitance component) depending on the electrode area.
Reactance: Impedance is expressed as a complex number. The real part is called resistance and the imaginary part is called reactance. The degree of phase change due to the capacitor or the inductance component, that is, their contribution at the total impedance is displayed.

Parallel Connection

Current passes through capacitance at high frequencies and through resistors at low frequencies.
The electrode interface can be equivalent to a parallel circuit.

Parallel Connection - Impedance Definition

If is large and R Xc , is close to  à Z = -Xc
If is low and R Xc , is close to  à Z = R

Warburg Impedance (Diffusion impedance)

Diffusion impedance is the solution resistance or charge transfer.
It does not have a constant value like a resistor, but its value changes with frequency variation.
Therefore, the diffusion coefficient of the ions is determined and evaluated.

Three phase contacts - Two contact surfaces

Phase Separation
For phase separation, phase changes should be observed in different frequency domains.

1. When the capacitances of two phases are the same

Interfaces with similar capacitances are difficult to distinguish.

2. When the capacitances of two phases are the same

The larger the capacitance difference between the two capacitors, the better the phase separation.
The capacity of the capacitor is related to the electrode (interface) area.

3. Phase separation order

The smaller the capacitance of the capacitor, the higher frequency is first phase-separated.

4. Even if the array of capacitors is arbitrary,


All resistances of the positive electrode, negative electrode and electrolyte of the cell are measured.

5. When the capacitance is small and disappears in the high-frequency range - it is not observed in the high-frequency range.

6. When the capacitance is large and disappears in the high-frequency range - it is not observed in the low-frequency range.


Diameter Determinants of Semicircle
The diameter of each semicircle depends only on the resistance (Zre).

Design of equivalent circuit through system analysis

How many interfaces are there?

1. Lead wire / Current collector 
2. Current collector / Anode (Li) 
3. Anode (Li) / Solution
4. Solution / Cathode 
5. Conducting agent / Active substance 
6. Ion / Active material, diffusion
7. Active material / Current collector 
8. Current collector / Conductor

Design of equivalent circuit


Simplified equivalent circuit  - I

Ignore the part where the resistance is too low.

Simplified equivalent circuit - II
1. Circuit deletion between wires with small contribution, current collector, and anode
2. Circuit simplification between cathode materials (conducting agent / active material interface)


Simplified equivalent circuit - III

Simplified equivalent circuit – IV


When the electronic conductivity at the contact surface is bad, it is observed as including the solution resistance.

Interpretation of Impedance Spectrum

 1. Impedance measurement
    Sample : SAFT LSH20 (Before/After Depassiavtion)
    Depassivation Method : 500 mA discharge (for 30 sec.)
    Experimental Condition : 100 kHz ~ 10 mHz
    DC potential : Open Circuit Voltage
    AC potential : 5 mV
2. Li/SOCl2 Battery internal system analysis


3. Equivalent circuit design

4. Equivalent circuit approximation through data