How to use AC impedance data to determine the diffusion coefficient of lithium electrical material?

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The lithium-ion battery is the migration and diffusion of Li + between the positive and negative poles, and the concentration difference of Li is established between the positive and negative electrodes, thereby storing electrical energy. Therefore, the diffusion between Li + between the positive and negative poles affects the performance of lithium ion battery performance. If we are sorted in various links from fast-to-slow speeds of Li +, there is no doubt that the diffusion of Li + in the electrolyte is the most.

Quick, followed by the charge exchange process of Li + in the positive and negative surface, the speed of this process is relatively slow, it is easy to limit the restriction mitigation, and Li + is the slowest in the positive and negative material, this The link is also often the key to restricting the magnification performance of lithium ion battery. As a key parameter solid phase diffusion coefficient of the reactive substance in the active substance, the solid phase diffusion coefficient is the key to the amount of material, but the parameters of the materials are not simple. Generally, the method of calculating the solid phase diffusion coefficient of the active material has an important potential titration, constant current titration, and AC impedance data.

Recently, Tienquangnguyen (First Servers) and Corneliabreitkopf (Corresponding Author) of Germany Dresden University of Technology proposed a new way to obtain diffusion coefficients through AC impedance data. The diffusion coefficient of acquiring materials using EIS data is not a new concept. There have been many models that have used a diffusion impedance value in AC impedance to calculate the diffusion coefficient of the electrode or material, but these models usually have to be combined with diffusion.

Calculation of parameters such as length, and this value is usually approximated by the electrode thickness or particle radius. The way Tienquangnguyen proposed only to use AC impedance data to obtain all parameters required to calculate the diffusion coefficient. According to the meaning of the diffusion coefficient, we can get a diffusion coefficient by the ratio between the diffusion length ID and the diffusion time taud (as shown in the following formula).

It can be seen from the above formula. To get a diffusion coefficient we have to get the above parameters by experiment data or theoretical model data. In the electrochemical system, ion mobility can be calculated based on the relaxation time tau2 in the thickness of the two-electric layer lambDAD and polarization.

In order to obtain the key parameters of the diffusion coefficient, we must first get the data of the diffusion layer thickness. The so-called diffusion layer refers to the range of material concentrations in the diffusion process, and the Bandaraampmellanderandcoelho et al. Et al.

Model to calculate the thickness of the diffusion layer. The figure below shows the impedance of the electrochemical system of the double blocking electrode and the loss angle normal value. The effective dielectric constant can be calculated by the following formula 3, where j is an imaginary unit, Delta is the ratio between half of the thickness of the sample and the thickness of the diffusion layer, usually we believe this value is greater than 10.

The loss angle is the ratio between dielectric loss and the real dielectric constant (shown in Formula 4). From the above figure B, it is possible to see that the loss angle node has a maximum value at the time constant TAU2, and the relationship between the loss angle normal value and Delta is shown in Formula 5, so the diffusion layer thickness can be calculated by the following formula 6. In the EIS data, the limited Warburg diffusion impedance contains parameters such as diffusion length, diffusion coefficient, and diffusion velocity, usually we can use an equivalent circuit to fit the EIS detection results by ZVIEW and other tools to obtain diffusion time parameters.

However, in some cases of some impedance, the fitting results are often less ideally, and this problem can be fitted to fit more accurate data by fitting a transition area in AC impedance data. The limited length Warburg diffusion impedance can be expressed in the formula 7, where RW is a limited diffusion impedance, and the diffusion time can be calculated by the above formula 1. The parameter relationship in the above formula is shown in the formulars 9, 10, and the solid and imaginary portion of the finite diffusion impedance may be simplified into the format of the following formula 13 by the following formula 11 and 12.

13 we can see that RW can mean the slope of the relational curve between Z and Omega1 / 2. The above figure shows a typical AC impedance map, which can see the slope of the impedance curve in the transition zone of 45 degrees from the figure, which means that the value of the real and imaginary part of the impedance in this region is equal. With regard to the diffusion process of the interface, we can fit the Randles equivalent circuit shown below.

Since the WARBURG element and the frequency square root and phase angle are negatively correlated, the pen direct decomposition contains the equivalent circuit of the Warburg element is still A very challenging work, so we can replace it as a parallel RW and CW, so the overall impedance of the equivalent circuit shown below is shown in Formula 15, and the total impedance real part is between When the frequency is approximately 0 as shown in Fig. 16, the real portion and the imaginary portion may be converted into a capacitance value of the two-electrical layer of the surface of the electrode surface in the form of the electrode surface in the form of the second formula 17, which is very small. Generally, in 1-10uf / cm2, the impedance of the total impedance in the following picture circuit can be considered equal to the imaginary part of the Warburg impedance, ie z = omGAZ, and the most important diffusion length ID of the diffusion coefficient can be electronically The diffusion coefficient and diffusion time are calculated (as shown in the following formula 19) assume that the charge of the charge is the same, so that the diffusion coefficient of the electrons can be replaced with ion mobility, and the diffusion time can be used The time constant corresponding to the arc at the highest point in the frequency curve shown in FIG.

Therefore, the above formula can be converted into the format shown in the formula. According to the above-mentioned model authors decomposes data from the literature, it can see the five samples selected from the following picture have a distinctive difference in the diffusion curve of the low frequency area, and several samples are composed of a semi-circular region. Then there is a limited diffusion impedance of about 45 degrees left and right in the range of relatively low frequencies, and therefore, according to the above model, the diffusion time constant of several models of the WSC = 2, 4, 5, 6 and 15 is 4, respectively.

16, 25, 36, and 225 (shown in Table 1 below). In order to compare the effects of the above model, the author takes the adsorption process of water molecules in the surface of the sulphate zirconium sulphate, first using the Randles equivalent circuit to fit the test detection results, and can see the real part of the impedance from the figure below. The error between the test value and the fitting value reached 25%, and the declaration of the circuit fitting effect containing Warburg impedance is not ideal in the case where high impedance or noise is relatively high.

Therefore, the numerical values ​​fit can only be Reference. In the figure below, the author compares the fitting effect of the model method proposed by the traditional equivalent circuit method and the author. From the lower left picture, it is necessary to see the fitting effect obtained by the new model method.

It is better than the traditional equivalent circuit. The diffusion coefficient obtained from the following Table 3 can see the result of net ion mobility and water vapor and the results of other people's detection. The method proposed by Tienquangnguyen fits by fitting the finite diffusion length portion in the AC impedance, the pen is straight and the length of the diffusion length, thereby realizing the rapid and accurate determination of fast and accurate data using AC impedance data.