电化学交流阻抗复数平面图和电容复数平面图上相似图形的等效电路变换规则(Ⅱ)──含有Warburg阻抗的等效电路的变换

Transfer Rule of Equivalent Circuits of Similar Plots on the Impedance Complex Plane and on the Capacitance Complex Plane for an AC Impedance Measurement(Ⅱ) Transferring of the Equivalent Circuits Containing the Warburg Impedance

提出并证明了等效电路中含有Warburg阻抗的电化学交流阻抗复数平面图和电容复数平面图上相似图形等效电路的变换规则 .推而广之 ,对任意包含有Warburg阻抗或其变换的等效电路 ,有着同样的变换规则 .应用此规则 ,可以将在一个复数平面图上的研究结果直接用到另一个复数平面图上 ,因此 ,变换规则是一种颇为有用的电化学交流阻抗研究的手段 .

The AC impedance technique is one of the important methods for electrochemical study. We have discovered that there is a certain transformation relationship between the equivalent circuits for similar plots on an impedance complex plane and on a capacitance complex plane. The transfer rule for an equivalent circuit being composed of the resistance and the capacitance has been given in our previous papers. Herein we give the transfer rule for an equivalent circuit including Warburg impedance as follows: for the equivalent circuit involving Warburg impedance, if we make the following transformation, (1) a resistance is substituted for a capacitance, and a capacitance for a resistance, (2) a Warburg impedance is changed to a Warburg transform, and a Warburg transform is changed to a Warburg impedance(the Warburg transform is expressed by a parallel connection of a resistance and a capacitance subjecting to the prerequisite of ωRC=1, R=Wω^-1/2 and 1/(ωC)=Wω^-1/2, here constant W is the proportional factor), and (3) a parallel connection is changed to a series connection, and a series connection to a parallel connection, then the plot on the Z″~Z′ plane for the original equivalent circuit and the plot on the C″~C′ plane for the transferred one, or the plot on the C″~C′ plane for the original equivalent circuit and the plot on the Z″~Z′ plane for the transferred one are similar, respectively. This means that impedance of the original equivalent circuit has the similar expression with capacitance of corresponding transferred one. Using the transfer rule the study results on a plot on one complex plane can be directly used to a similar plot on another complex plane. Therefore, the transfer rule is a useful tool for the AC impedance study.