Visual Simulation (II) of EIS Test Process
Release time:
2023-08-17
Continuing the visualization of the EIS test process, the basic circuit model was talked about last time, and this time it starts with the Randles circuit model.
Continuing the visualization of the EIS test process, the basic circuit model was talked about last time, and this time it starts with the Randles circuit model.
1 Randles model
The Randles model is one of the very representative models in electrochemical research, which was proposed by the British chemist Derek A. Randles in 1947. It is composed of solution bulk resistance Ri, electric double layer capacitance Cdl and charge transfer resistance Rct, as shown in the figure below.
The visual code is as follows:
R=5 #Ohm
Cdl=20e-6 #F
Rct=75 #Ohm
F = np.logspace(5,-2,80) # HZ
W = 2 *np.pi*f
Z = Ri 1/(1/Rct 1j * w * Cdl)
fig=plt.figure(figsize=(15,8))
ax1=fig.add_subplot(231)
ax2=fig.add_subplot(232)
ax3=fig.add_subplot(233)
ax4=fig.add_subplot(223)
ax5=fig.add_subplot(224)
Ax1.plot (Z.real,-Z.imag,'r-')
Ax2.plot (f,-Z.imag,'b-')
Ax3.plot (f,Z.real,'c-')
Ax4.plot (f,abs(Z),'g-')
Ax5.plot (f,-np.angle(Z)/np. pl * 180,'m-')
Ani_this ()
Point1,=ax1.plot(np.real(Z)[0],-np.imag(Z)[0],'ro')
Point2,=ax2.plot(f[0],-np.imag(Z)[0],'bo')
point3,=ax3.plot(f[0],np.real(Z)[0],'co')
Point4, = ax4.plot(f[0],abs(Z)[0],'go')
Point5, = ax5.plot(f[0],-np.angle(Z)[0]/np. ft * 180,'mo')
ani = animation.FuncAnimation(fig=fig,func=update,blit=True,frames=np.arange(0,21),interval=1000)
plt.show()
The results are shown in the following figure:
It can be seen that the semi-circle diameter of the Nyquist graph reflects the size of the electrochemical process resistance Rct on the electrode surface. The magnitude of the intercept of the semicircle with the real axis at high frequencies reflects the electrolyte resistance Ri. As the frequency increases, the electrochemical reaction is gradually dominated by Ri.
2 Randles-Warburg模型
However, the above circuit model does not consider the diffusion process, diffusion in the electrochemical process is often the speed of the step, can not be ignored. The following is the equivalent circuit of Randles-Warburg combination:
For such a planar electrode Faraday reaction controlled by a semi-infinite diffusion process, the visualization code is as follows:
R=5 #Ohm
Cdl=20e-6 #F
Rct=75 #Ohm
sigma=10
F = np.logspace(5,-2,80) # HZ
W = 2 *np.pi*f
Zw = sigma *(w **(-0.5)-1j * w **(-0.5))
Z = Ri 1/(1/(Rct Zw) 1j * w * Cdl)
The Nyquist graph has a 45 ° straight line in the low frequency region, and the Bode graph is also very different from the Randles model in the low frequency region.
Reduce the low frequency cut-off frequency by 1 order of magnitude, from 0.01Hz to 0.001Hz, to see what changes have been made.
R=5 #Ohm
Cdl=20e-6 #F
Rct=75 #Ohm
sigma=10
F = np.logspace(5,-3,80) # HZ
W = 2 *np.pi*f
Zw = sigma *(w **(-0.5)-1j * w **(-0.5))
Z = Ri 1/(1/(Rct Zw) 1j * w * Cdl)、
Diffusion mainly affects the impedance behavior in the low frequency region, and for various batteries, the actual operating conditions are usually in the low frequency region, so the impedance brought by * diffusion is very important, and it is also a problem that has been plagued by the research and development of batteries and materials.
There are many kinds of diffusion impedance, here only consider the Warburg impedance, that is, semi-infinite diffusion (semi-infinite), more detailed various diffusion models are described in subsequent articles.
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