Battery pole piece flexibility detection method and device

Abstract

The invention discloses a battery pole piece flexibility detection method and device, and the method comprises the steps: measuring the initial multi-band impedance spectrum of a pole piece, and carrying out the fitting to obtain the interface contact impedance and the impedance between active substance particles; bending and deforming the pole piece; measuring the impedance spectrum of the bent pole piece, calculating the change rate of interface contact impedance and the change rate of body impedance between active substance particles, and judging the flexibility level of the pole piece according to the range of the change rate of interface contact impedance and the change rate of body impedance between active substance particles; the method has the advantages that the flexibility of the lithium battery pole piece can be comprehensively detected and evaluated, and quality monitoring in battery production is guided.

Description

Technical Field

[0001] This invention relates to the field of lithium-ion battery technology, specifically to a method and apparatus for testing the flexibility of battery electrodes. Background Technology

[0002] Lithium-ion batteries mainly consist of three parts: electrodes (positive and negative electrodes), electrolyte, and separator. The generation and transfer of energy mostly occur in the electrode area; therefore, the performance of the electrodes directly determines the performance of the battery. Electrode flexibility is affected by factors such as raw material characteristics, coating, rolling, and baking processes. Electrodes with different levels of flexibility are suitable for different types of manufacturing processes, resulting in different types of batteries. Poorly flexible electrodes affect the quality of the winding process, leading to economic losses, and are prone to breakage, resulting in aluminum foil burrs and film powder shedding, thus affecting the safety performance of the battery cell. Therefore, the testing of battery electrode flexibility is of great significance for battery preparation and production. Traditional mechanical tests (such as folding and bending methods) can only qualitatively assess macroscopic mechanical properties and cannot detect the impact of microscopic cracks on the conductive network. For example, the bending test method and equipment for flexible batteries disclosed in Chinese Patent Publication No. CN108801817A belongs to the bending test method. DC resistance method: It only provides a global resistance value and cannot distinguish between damage at the current collector-active material interface and network breakage between particles. Therefore, traditional mechanical testing methods cannot detect and evaluate the flexibility of lithium battery electrodes, making it difficult to guide quality monitoring in battery production. Summary of the Invention

[0003] The technical problem that this invention aims to solve is that existing technologies cannot comprehensively test and evaluate the flexibility of lithium battery electrodes, making it difficult to guide quality monitoring in battery production.

[0004] This invention solves the above-mentioned technical problems through the following technical means: a method for testing the flexibility of battery electrodes, comprising: S1. Measure the initial multi-band impedance spectrum of the electrode and obtain the interfacial contact impedance and the interparticle volume impedance of the active material by fitting. S2. Bend and deform the electrode sheet; S3. Measure the impedance spectrum after bending the electrode, calculate the rate of change of interfacial contact impedance and the rate of change of interparticle impedance of active material, and determine the flexibility level of the electrode based on the range of the rate of change of interfacial contact impedance and the rate of change of interparticle impedance of active material.

[0005] This invention utilizes the change rate of surface contact impedance and the change rate of interparticle volume impedance of active material obtained before and after electrode bending deformation to evaluate the flexibility level of a fixed electrode. Among them, the surface contact impedance reflects the degree of interface peeling of the electrode, and the interparticle volume impedance of active material reflects the degree of breakage of the active material particle network of the electrode. Thus, it can detect the impact of micro-cracks in the electrode on the conductive network, and also distinguish between current collector-active material interface damage and interparticle network breakage. It can comprehensively and accurately evaluate the flexibility of the electrode, which is convenient for guiding quality monitoring in battery production.

[0006] Furthermore, prior to step S1, the electrode is pre-processed. The pre-processing process involves removing the electrode to be tested, cutting the electrode to a preset size, and welding copper leads to both ends of the electrode.

[0007] Furthermore, the initial multi-band impedance spectrum of the measured electrode includes: An electrochemical workstation was used to test the impedance of the electrode at different frequencies. The interfacial contact impedance was obtained by fitting the impedance in the high-frequency region, and the interparticle volume impedance of the active material was obtained by fitting the impedance in the low-frequency region.

[0008] Furthermore, the frequency range of the electrochemical workstation is 0.1Hz-1MHz, and the amplitude is 10mV.

[0009] Furthermore, the frequency range of the high-frequency region is 1kHz-1MHz, and the frequency range of the low-frequency region is 0.1Hz-1kHz.

[0010] Furthermore, when bending the electrode sheet, the applied bending angle range is 90°-360°, and the radius of curvature is 1~3mm.

[0011] Furthermore, the interfacial contact impedance reflects the degree of interfacial peeling of the electrode; the greater the interfacial contact impedance, the greater the degree of interfacial peeling of the electrode. The interparticle impedance of the active material reflects the degree of breakage of the active material particle network of the electrode; the greater the interparticle impedance of the active material, the greater the degree of breakage of the active material particle network of the electrode.

[0012] Furthermore, the determination of the electrode's flexibility level based on the range of the interfacial contact impedance change rate and the interparticle bulk impedance change rate of the active material includes: If ΔRc≤5% and ΔRbulk≤10%, the electrode is considered to have excellent flexibility; if 5%<ΔRc≤20% and 10%<ΔRbulk≤20%, the electrode is considered to have qualified flexibility; if ΔRc>20% or ΔRbulk>20%, the electrode is considered to have substandard flexibility. Here, ΔRc represents the rate of change of interfacial contact resistance, and ΔRbulk represents the rate of change of interparticle bulk resistance of active material.

[0013] Furthermore, the ΔRc = (Rc 弯曲后 - Rc 弯曲前 ) / Rc 弯曲前 ×100%; ΔRbulk = (Rbulk) 弯曲后 -Rbulk 弯曲前 ) / Rbulk 弯曲前 ×100%; where Rc 弯曲后 Rc represents the interfacial contact resistance after the electrode is bent. 弯曲前 Rbulk represents the interface contact resistance before the electrode is bent. 弯曲后 Rbulk represents the interparticle bulk impedance of the active material after the electrode is bent. 弯曲前 This indicates the interparticle impedance of the active material before the electrode is bent.

[0014] The present invention also provides a battery electrode flexibility testing device, comprising: The first test module is used to measure the initial multi-band impedance spectrum of the electrode and to obtain the interfacial contact impedance and the interparticle volume impedance of the active material. Bending deformation module, used to bend and deform the electrode sheet; The second testing module is used to measure the impedance spectrum of the electrode after bending, calculate the rate of change of interfacial contact impedance and the rate of change of interparticle impedance of active material, and determine the flexibility level of the electrode based on the range of the rate of change of interfacial contact impedance and the rate of change of interparticle impedance of active material.

[0015] Furthermore, the first test module preprocesses the electrode sheet, which involves removing the electrode sheet to be tested, cutting the electrode sheet to a preset size, and welding copper leads to both ends of the electrode sheet.

[0016] Furthermore, the initial multi-band impedance spectrum of the measured electrode includes: An electrochemical workstation was used to test the impedance of the electrode at different frequencies. The interfacial contact impedance was obtained by fitting the impedance in the high-frequency region, and the interparticle volume impedance of the active material was obtained by fitting the impedance in the low-frequency region.

[0017] Furthermore, the frequency range of the electrochemical workstation is 0.1Hz-1MHz, and the amplitude is 10mV.

[0018] Furthermore, the frequency range of the high-frequency region is 1kHz-1MHz, and the frequency range of the low-frequency region is 0.1Hz-1kHz.

[0019] Furthermore, when bending the electrode sheet, the applied bending angle range is 90°-360°, and the radius of curvature is 1~3mm.

[0020] Furthermore, the interfacial contact impedance reflects the degree of interfacial peeling of the electrode; the greater the interfacial contact impedance, the greater the degree of interfacial peeling of the electrode. The interparticle impedance of the active material reflects the degree of breakage of the active material particle network of the electrode; the greater the interparticle impedance of the active material, the greater the degree of breakage of the active material particle network of the electrode.

[0021] Furthermore, the determination of the electrode's flexibility level based on the range of the interfacial contact impedance change rate and the interparticle bulk impedance change rate of the active material includes: If ΔRc≤5% and ΔRbulk≤10%, the electrode is considered to have excellent flexibility; if 5%<ΔRc≤20% and 10%<ΔRbulk≤20%, the electrode is considered to have qualified flexibility; if ΔRc>20% or ΔRbulk>20%, the electrode is considered to have substandard flexibility. Here, ΔRc represents the rate of change of interfacial contact resistance, and ΔRbulk represents the rate of change of interparticle bulk resistance of active material.

[0022] Furthermore, the ΔRc = (Rc 弯曲后 - Rc 弯曲前 ) / Rc 弯曲前 ×100%; ΔRbulk = (Rbulk) 弯曲后 -Rbulk 弯曲前 ) / Rbulk 弯曲前 ×100%; where Rc 弯曲后 Rc represents the interfacial contact resistance after the electrode is bent. 弯曲前 Rbulk represents the contact resistance at the interface before the electrode is bent. 弯曲后 Rbulk represents the interparticle bulk impedance of the active material after the electrode is bent. 弯曲前 This indicates the interparticle impedance of the active material before the electrode is bent.

[0023] The advantages of this invention are: (1) The present invention uses the change rate of surface contact impedance and the change rate of interparticle volume impedance of active material obtained by testing before and after the electrode bending deformation to evaluate the flexibility level of the electrode. Among them, the interface contact impedance can reflect the degree of interface peeling of the electrode, and the interparticle volume impedance of active material can reflect the degree of breakage of the active material particle network of the electrode. Thus, it can detect the influence of microcracks of the electrode on the conductive network, and can also distinguish between current collector-active material interface damage and interparticle network breakage. It can comprehensively and accurately evaluate the flexibility of the electrode, which is convenient for guiding quality monitoring in battery production.

[0024] (2) After cutting the electrode, copper leads are welded to both ends of the electrode to eliminate the influence of contact resistance, thereby further improving the accuracy of the detection method.

[0025] (3) This invention achieves a “mechanical-electrochemical” synergistic evaluation of electrode flexibility through “frequency band separation impedance analysis”, which has the advantages of high precision and low cost. It can be widely used in lithium battery electrode process development, quality monitoring and failure analysis, providing key technical support for high consistency manufacturing.

[0026] (4) The document CN108801817A in the background art describes the bending test of a complete flexible battery in the presence of electrolyte, where the impedance change mainly reflects the change in the ion conduction path. This invention, however, targets dry electrodes (without electrolyte filling), analyzing the integrity of the electron conduction network through multi-band impedance spectroscopy. This not only detects the impact of micro-cracks on the conductive network but also distinguishes between current collector-active material interface damage and interparticle network breakage. The two are fundamentally different in technical field, test object, and physical mechanism. This invention solves the quality control problem of dry electrodes during the manufacturing process, which is completely different from the application scenario described in the background art document.

[0027] (5) This invention takes into account that high-frequency current tends to conduct on the surface of the current collector and in the adjacent active material interface layer, and the impedance of this frequency band is extremely sensitive to the contact state between the current collector and the active material. Low-frequency current can penetrate the entire active material coating, and its conduction path depends entirely on the conductive network formed between the active material particles. The impedance of this frequency band is extremely sensitive to the contact state between particles and the network connectivity. Therefore, this invention uses impedance fitting in the high-frequency region to form the interface contact impedance Rc, and uses impedance fitting in the low-frequency region to form the interparticle bulk impedance Rbulk of the active material. Attached Figure Description

[0028] Figure 1 This is the equivalent circuit model of the electrode sheet in the battery electrode sheet flexibility testing method disclosed in the embodiments of the present invention; Figure 2 This is a comparison of Nyquist images before and after bending in a battery electrode flexibility testing method disclosed in an embodiment of the present invention. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0030] Example 1 like Figure 1 and Figure 2As shown, Embodiment 1 of the present invention provides a method for testing the flexibility of battery electrodes, comprising: S1. Measure the initial multi-band impedance spectrum of the electrode and fit it to obtain the interfacial contact impedance Rc and the interparticle bulk impedance Rbulk of the active material. In this embodiment, the electrode is pre-treated before testing. The pre-treatment process involves taking the electrode to be tested, cutting it to a standardized size (50mm × 10mm), and welding copper leads to both ends to eliminate the influence of contact resistance. The initial multi-band impedance spectrum is measured using an electrochemical workstation (frequency range: 0.1Hz-1MHz, amplitude: 10mV). The impedance at different frequencies is measured, and the interfacial contact impedance Rc is formed by fitting the impedance in the high-frequency region, and the interparticle bulk impedance Rbulk of the active material is formed by fitting the impedance in the low-frequency region. The frequency range of the high-frequency region is 1kHz-1MHz, and the frequency range of the low-frequency region is 0.1Hz-1kHz. The interfacial contact impedance Rc and the interparticle bulk impedance Rbulk of the active material are obtained by fitting the measured full-band impedance spectrum data using professional impedance data analysis software (such as ZView, equivalent circuit fitting software). High-frequency current tends to conduct on the surface of the current collector and in the adjacent active material interface layer. Therefore, the impedance in this frequency band is extremely sensitive to the contact state between the current collector and the active material. Based on this physical phenomenon, this invention defines "interfacial contact impedance (Rc)" to specifically characterize the quality of interfacial bonding. Low-frequency currents can penetrate the entire active material coating, and their conduction path depends entirely on the conductive network formed between the active material particles. Therefore, the impedance in this frequency band is extremely sensitive to the contact state between particles and the network connectivity. Based on this physical phenomenon, this invention defines "interparticle bulk impedance (Rbulk)" to specifically characterize the integrity of the particle network.

[0031] S2. Bend and deform the electrode sheet; Specifically, bend the electrode sheet to be tested. The radius of curvature can be set to R=1, 2, 3 mm. Apply a bending angle of 90°-360° to the electrode sheet and bend the electrode sheet at a certain speed.

[0032] S3. Measure the impedance spectrum after bending the electrode, calculate the rate of change of interfacial contact impedance ΔRc and the rate of change of interparticle impedance of active material ΔRbulk, and determine the flexibility level of the electrode based on the range of these two rates. The interfacial contact impedance Rc reflects the degree of interfacial peeling of the electrode; the larger the Rc, the greater the degree of interfacial peeling. The interparticle impedance Rbulk reflects the degree of breakage of the active material particle network of the electrode; the larger the Rbulk, the greater the degree of breakage. Therefore, if ΔRc≤5% and ΔRbulk≤10%, the electrode is judged to have excellent flexibility; if 5%<ΔRc≤20% and 10%<ΔRbulk≤20%, the electrode is judged to have qualified flexibility; if ΔRc>20% or ΔRbulk>20%, the electrode is judged to have substandard flexibility. Here, ΔRc represents the rate of change of interfacial contact resistance, and ΔRbulk represents the rate of change of interparticle bulk resistance of active material.

[0033] Where, ΔRc = (Rc 弯曲后 - Rc 弯曲前 ) / Rc 弯曲前 ×100%; ΔRbulk = (Rbulk) 弯曲后 -Rbulk 弯曲前 ) / Rbulk 弯曲前 ×100%; where Rc 弯曲后 Rc represents the interfacial contact resistance after the electrode is bent. 弯曲前 Rbulk represents the contact resistance at the interface before the electrode is bent. 弯曲后 Rbulk represents the interparticle bulk impedance of the active material after the electrode is bent. 弯曲前 This indicates the interparticle impedance of the active material before the electrode is bent.

[0034] like Figure 1 The figure shows the equivalent circuit model of the electrode. Figure 1 In this diagram, Rs represents the current collector resistance, and CPE1 and CPE2 are two different constant phase angle elements. To verify the effectiveness of this invention, a lithium iron phosphate battery with a positive electrode ratio of SP:conductive slurry:PVDF of 97:0.5:0.5:2 was used; the slurry was prepared using NMP solvent, and the coating surface density was 400 g / m²; impedance spectra were tested; the electrode was also bent with a radius of curvature of 1 mm and a bending speed of 0.1 m / s. The data before and after bending the positive electrode are compared in Table 1 below.

[0035] Table 1 Comparison of Test Data Before and After Bending the Positive Electrode

[0036] Table 1 shows that ΔRc = 216%, indicating interfacial peeling, and ΔRbulk = 200%, indicating particle network fracture, thus indicating that the electrode flexibility does not meet the standard. Combined with... Figure 2 As shown, the increased diameter of the semicircle in the high-frequency region indicates interface peeling, while the change in the slope of the oblique line in the low-frequency region indicates the breakage of the particle network.

[0037] Through the above technical solutions, this invention sensitively captures the decrease in the adhesion between the current collector and the dressing using high-frequency impedance (1kHz-1MHz), solving the problem that traditional folding methods cannot quantify micron-level interface delamination. It reflects internal cracks in the active material layer using low-frequency impedance (0.1Hz-1kHz), which is more than 10 times more sensitive than the DC resistance method. By defining a flexibility qualification threshold (e.g., ΔRc≤10%, ΔRbulk≤20%), it replaces the subjective judgment of "no visible cracks". Thus, the overall solution achieves a synergistic "mechanical-electrochemical" evaluation of electrode flexibility through "frequency band separated impedance analysis".

[0038] Example 2 Based on Embodiment 1, Embodiment 2 of the present invention also provides a battery electrode flexibility testing device, comprising: The first test module is used to measure the initial multi-band impedance spectrum of the electrode and to obtain the interfacial contact impedance and the interparticle volume impedance of the active material. Bending deformation module, used to bend and deform the electrode sheet; The second testing module is used to measure the impedance spectrum of the electrode after bending, calculate the rate of change of interfacial contact impedance and the rate of change of interparticle impedance of active material, and determine the flexibility level of the electrode based on the range of the rate of change of interfacial contact impedance and the rate of change of interparticle impedance of active material.

[0039] Specifically, the first test module preprocesses the electrode sheet, which involves removing the electrode sheet to be tested, cutting the electrode sheet to a preset size, and welding copper leads to both ends of the electrode sheet.

[0040] Specifically, the measurement of the initial multi-band impedance spectrum of the electrode includes: An electrochemical workstation was used to test the impedance of the electrode at different frequencies. The interfacial contact impedance was obtained by fitting the impedance in the high-frequency region, and the interparticle volume impedance of the active material was obtained by fitting the impedance in the low-frequency region.

[0041] More specifically, the frequency range of the electrochemical workstation is 0.1Hz-1MHz, and the amplitude is 10mV.

[0042] More specifically, the frequency range of the high-frequency region is 1kHz-1MHz, and the frequency range of the low-frequency region is 0.1Hz-1kHz.

[0043] Specifically, when bending and deforming the electrode, the applied bending angle range is 90°-360°, and the radius of curvature is 1~3mm.

[0044] Specifically, the interfacial contact impedance reflects the degree of interfacial peeling of the electrode; the greater the interfacial contact impedance, the greater the degree of interfacial peeling of the electrode. The interparticle impedance of the active material reflects the degree of breakage of the active material particle network of the electrode; the greater the interparticle impedance, the greater the degree of breakage of the active material particle network of the electrode.

[0045] More specifically, determining the flexibility level of the electrode based on the range of the interfacial contact impedance change rate and the interparticle bulk impedance change rate of the active material includes: If ΔRc≤5% and ΔRbulk≤10%, the electrode is considered to have excellent flexibility; if 5%<ΔRc≤20% and 10%<ΔRbulk≤20%, the electrode is considered to have qualified flexibility; if ΔRc>20% or ΔRbulk>20%, the electrode is considered to have substandard flexibility. Here, ΔRc represents the rate of change of interfacial contact resistance, and ΔRbulk represents the rate of change of interparticle bulk resistance of active material.

[0046] More specifically, the ΔRc = (Rc 弯曲后 - Rc 弯曲前 ) / Rc 弯曲前 ×100%; ΔRbulk = (Rbulk) 弯曲后 -Rbulk 弯曲前 ) / Rbulk 弯曲前 ×100%; where Rc 弯曲后 Rc represents the interfacial contact resistance after the electrode is bent. 弯曲前 Rbulk represents the contact resistance at the interface before the electrode is bent. 弯曲后 Rbulk represents the interparticle bulk impedance of the active material after the electrode is bent. 弯曲前 This indicates the interparticle impedance of the active material before the electrode is bent.

[0047] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for testing the flexibility of battery electrodes, characterized in that, include: S1. Measure the initial multi-band impedance spectrum of the electrode and obtain the interfacial contact impedance and the interparticle volume impedance of the active material by fitting. S2. Bend and deform the electrode sheet; S3. Measure the impedance spectrum after bending the electrode, calculate the rate of change of interfacial contact impedance and the rate of change of interparticle impedance of active material, and determine the flexibility level of the electrode based on the range of the rate of change of interfacial contact impedance and the rate of change of interparticle impedance of active material.

2. The method for testing the flexibility of battery electrodes according to claim 1, characterized in that, Before step S1, the electrode is pre-processed. The pre-processing process involves removing the electrode to be tested, cutting the electrode to a preset size, and welding copper leads to both ends of the electrode.

3. The method for testing the flexibility of battery electrodes according to claim 1, characterized in that, The measurement of the initial multi-band impedance spectrum of the electrode includes: An electrochemical workstation was used to test the impedance of the electrode at different frequencies. The interfacial contact impedance was obtained by fitting the impedance in the high-frequency region, and the interparticle volume impedance of the active material was obtained by fitting the impedance in the low-frequency region.

4. The method for testing the flexibility of battery electrodes according to claim 3, characterized in that, The frequency range of the electrochemical workstation is 0.1Hz-1MHz, and the amplitude is 10mV.

5. The method for testing the flexibility of battery electrodes according to claim 3, characterized in that, The frequency range of the high-frequency region is 1kHz-1MHz, and the frequency range of the low-frequency region is 0.1Hz-1kHz.

6. The method for testing the flexibility of battery electrodes according to claim 1, characterized in that, When bending the electrode sheet, the applied bending angle range is 90°-360°, and the radius of curvature is 1~3mm.

7. The method for testing the flexibility of battery electrodes according to claim 1, characterized in that, The interfacial contact impedance reflects the degree of interfacial peeling of the electrode; the greater the interfacial contact impedance, the greater the degree of interfacial peeling of the electrode. The interparticle impedance of the active material reflects the degree of breakage of the active material particle network of the electrode; the greater the interparticle impedance, the greater the degree of breakage of the active material particle network of the electrode.

8. The method for testing the flexibility of battery electrodes according to claim 7, characterized in that, The determination of the electrode flexibility level based on the range of interfacial contact impedance change rate and interparticle bulk impedance change rate of active material includes: If ΔRc≤5% and ΔRbulk≤10%, the electrode is considered to have excellent flexibility; if 5%<ΔRc≤20% and 10%<ΔRbulk≤20%, the electrode is considered to have qualified flexibility; if ΔRc>20% or ΔRbulk>20%, the electrode is considered to have substandard flexibility. Here, ΔRc represents the rate of change of interfacial contact resistance, and ΔRbulk represents the rate of change of interparticle bulk resistance of active material.

9. The method for testing the flexibility of battery electrodes according to claim 8, characterized in that, The ΔRc =(Rc 弯曲后 - Rc 弯曲前 ) / Rc 弯曲前 ×100%; ΔRbulk = (Rbulk) 弯曲后 - Rbulk 弯曲前 ) / Rbulk 弯曲前 ×100%; where Rc 弯曲后 Rc represents the interfacial contact resistance after the electrode is bent. 弯曲前 Rbulk represents the contact resistance at the interface before the electrode is bent. 弯曲后 Rbulk represents the interparticle bulk impedance of the active material after the electrode is bent. 弯曲前 This indicates the interparticle impedance of the active material before the electrode is bent.

10. A device for testing the flexibility of battery electrodes, characterized in that, include: The first test module is used to measure the initial multi-band impedance spectrum of the electrode and to obtain the interfacial contact impedance and the interparticle volume impedance of the active material. Bending deformation module, used to bend and deform the electrode sheet; The second testing module is used to measure the impedance spectrum of the electrode after bending, calculate the rate of change of interfacial contact impedance and the rate of change of interparticle impedance of active material, and determine the flexibility level of the electrode based on the range of the rate of change of interfacial contact impedance and the rate of change of interparticle impedance of active material.

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