Mathematical Model of Four-Line Probe to Determine Conductive Properties of Thin-Film Battery Electrodes

Abstract

Measurement of the electronic conductivity of porous thin-film battery electrodes poses significant challenges, particularly when the film is attached to a metallic current collector. We have developed a micro-four-line probe and testing procedure that overcomes many of these difficulties while relying on principles similar to commonly used four-point probes. This work describes a mathematical model that enables rapid inversion of the data collected by such experiments to compute two properties: bulk electronic conductivity of the film and contact resistance with the current collector. The model accounts for variable probe and sample geometry and variable resistance between the probe and the sample. Results from 2D and 3D models are presented. The full 3D model combines a Fourier series with the boundary element method to generate a solution that requires significantly less computational cost than a corresponding finite element solution for the same level of accuracy. The model confirms that the ideal probe line spacing is close to the value of the electrode film thickness. Transportation, communication, and mobile electronics are just a few of the many industries that are relying increasingly on battery technology. Lithium-ion batteries that employ particle-based thin-film electrodes are a critical part of this technological advance. However, such electrodes can exhibit conductivity limitations, including significant spatial variations due to particle and composition inhomogeneities, which can cause so-called hot and cold spots, undesired sidereactions, and an overall decrease in cell performance and safety. [1][2][3] One key to resolving such manufacturing and materials problems is accurate measurement of relevant properties. The general approach for conductive properties is to perturb the sample with an imposed current and then measure the electric potential on two or more points on the surface. However, it is surprisingly difficult to accurately measure the electrical conductivity and contact resistance (between electrode and current collector) of these films. [4][5][6][7][8][9] This is because the contact resistance between probe and sample is high relative to the resistance of the sample, the sample is mechanically fragile, and the conductivity of the electrode film is confounded by the presence of a highly conductive adjacent metal layer (the current collector). The electrode film can be delaminated from the current collector in order to eliminate the last problem, 4 though it is more desirable to measure electrodes non-destructively as is proposed in this work.Conductive property measurements.-Multiple methods have been used in the past to measure the conductivity or resistivity of thin films or layered materials. The four-point-probe method has been in use for many decades, and is particularly useful in measuring singlelayer conductive materials. On the other hand, with point probes it is difficult to control the pressure imparted to the electrode material during the measurement, which can change conduc...

Micro-Four-Line Probe to Measure Electronic Conductivity and Contact Resistance of Thin-Film Battery Electrodes

“…It was found that, as a general rule, the distance between the two outer lines of the probe should be approximately the same as the sample film thickness. 1 With the above considerations in mind, the lines were designed to be 10 μm wide and 3 mm long, with 10 μm spacing between them, as shown in Fig. 1.…”

“…13 The probe template was designed to yield 10 μm wide lines, but because of nearly isotropic electroplating on the sides as well as the tops of the lines, at the completion of the process the lines had widened to 12 μm. Practical adaptation of mathematical model.-As specified by the mathematical model, 1 two different electrical configurations must be used with the μ4LP to estimate the bulk conductivity and interfacial resistance. The configurations are referred to as the tangential and orthogonal experiments.…”

Self-Healing, Flexible and Smart 3D Hydrogel Electrolytes Based on Alginate/PEDOT:PSS for Supercapacitor Applications

“…The peak at 1620 cm −1 for alginate/PEDOT:PSS is attributed to the expansion of vibrations of -C=N groups, which are produced through the chemical reaction of -OH in oxidized starch and H 2 N - in starch from wheat. In addition, the peak at 1326 cm −1 is attributed to alginate with bending oscillations -CH,–SO 3 or -N-CO-CH 2 - groups, which are from alginate/PEDOT:PSS [ 33 , 34 , 35 , 36 , 37 , 38 , 39 , 42 ].…”

“…The electrical resistance (R) of each gel was measured during drying using a four-line probe method. The resistance of the plate was determined using the following equation [ 42 ]: where w is the width of the sample (2.5 cm) and d is the spacer between the leads (0.35 cm).…”

High Sulfur Content of Mesoporous Activated Carbon Composite Derived from Water Hyacinth

“…The electrical conductivity measurements of both ACWH and ACWH/S samples were carried out using the four-line probe method at room temperature. A current variation of 0.01-0.05 mA from a DC source is applied to the two outer probes, and then the resulting voltage is measured at the two inner probes with a digital multimeter [25,26]. Based on the current and voltage curves, the resistivity and conductivity values can be determined.…”