Method for the measurement of triboelectric charge transfer at solid–liquid interface

Triboelectrification between a liquid and a solid is a common phenomenon in our daily life and industry. Triboelectric charges generated at liquid/solid interfaces have effects on energy harvesting, triboelectrification-based sensing, interfacial corrosion, wear, lubrication, etc. Knowing the amount of triboelectric charge transfer is very useful for studying the mechanism and controlling these phenomena, in which an accurate method is absolutely necessary to measure the triboelectric charge generated at the solid—liquid interface. Herein, we established a method for measuring the charge transfer between different solids and liquids. An equipment based on the Faraday cup measurement was developed, and the leakage ratio (rl) was quantified through simulation based on an electrostatic field model. Typical experiments were conducted to validate the reliability of the method. This work provides an effective method for charge measurement in triboelectrification research.

Currently, several methods have been developed to measure triboelectric charges. One of them is the electrode induction method, which is based on the electrostatic induction effect [2,[24][25][26][27]. Generally, the triboelectric charge generated on the surface of the material will generate an inducted potential on the back electrode of the sample. By measuring the induced potential and the corresponding current, triboelectric charges can be calculated by integrating the current with time. Zheng et al. [2] proposed a water-drop triboelectric nanogenerator and measured electric signals generated in triboelectrification between polytetrafluoroethylene (PTFE) and raindrop based on the electrode induction method. Zhang et al. [8] used the electrode induction method to measure the electric signals generated during the friction process between the dopamine-modified PTFE filter membrane and the mixture of water and organic matter (such as ethanol). Nahian et al. [28] used the electrode induction method to measure the electric signals generated in contact-electrification between PTFE and deionized (DI) water for studying the effect of surface-hydrophobicity and roughness on triboelectric performance. Zou et al. [29] built up an apparatus based on the electrode induction method to measure charge transfer between polymers and liquid mercury (Hg). Copper (Cu) is deposited on the back of the tested polymer materials as an electrode, and the other electrode is liquid metallic Hg. When the tested material contacts and separates with Hg, there is potential difference generating between the Cu and Hg electrodes. Usually, there is electric resistance in the measuring circuit, and the calculated value of the charge based on the measured current is usually smaller than that of the generated charge [30], leading to the error of charge measurement. The Kelvin probe force microscope (KPFM), which is based on the atomic force microscope (AFM), can also be used for the measurement of solid-liquid triboelectric charge. Lin et al. [16] utilized the KPFM to measure the surface potential and charge density of ceramic thin films after they contact with different aqueous solution. Triboelectric charges on silica (SiO 2 ) surfaces with different functional groups after rubbing with DI water and organic solution were also measured by using the KPFM method [15]. A major problem in potential measurement with the KPFM method is the influence of ions in the liquid. On the one hand, the measurement of surface potential will be affected by the shielding effect of the electric double layer (EDL) formed at the interface between probe and liquid and sample surface and liquid [31]. On the other hand, when using the KPFM method to measure the surface potential, a bias is usually applied to the probe or the sample, and the ions in the liquid will move due to the bias voltage [32,33]. As a consequence, the properties of the solution and the EDL will change, resulting in the measurement error of surface potential. Besides, when using the KPFM method, the sample surface must be very smooth (the surface roughness (R a ) is less than 50 nm), which limited the application of this method. In addition to the above-mentioned two methods, the Faraday cup method is also used for the measurement of electrostatic charges generated in triboelectrification between solids and liquids. The Faraday cup can be used for the real-time measurement of charge [34], and there is no limitation on the sample size. Choi et al. [35] Friction 11(8): 1544-1556 (2023) | https://mc03.manuscriptcentral.com/friction reported their work by using the Faraday cup method to measure the triboelectric charges of droplets containing bio-molecules after rubbing with a pipette and found that triboelectric charges on the droplet can affect the chemical characteristics of solution and influence the combination and localization of charged bio-molecules. Cezan et al. [36] put PTFE beads into hexane solution in a glass vial and shaked the glass vial using a vortexer for 0.5-2 min, and then used the Faraday cup to measure the triboelectric charge generated on the PTFE beads. However, since the Faraday cup is usually open, its non-closed nature will cause charge leakage. For most of the research, the charge leakage was basically not taken into account, which led to the inaccuracy of the measurement. If charge leakage is quantified, the Faraday cup method can be an accurate method for charge measurement and will be intensively employed in many cases.
In this paper, a method for measuring triboelectric charge between solids and liquids was introduced, and equipment based on this method was built. A special Faraday cup was designed, and a method for calculating the leakage ratio was proposed. Based on the leakage ratio simulation, the size of the Faraday cup was optimized, and the design criteria for Faraday cup size selection were summarized. Triboelectrification experiments between several insulating and conducting solids and liquids were performed to validate the method.

Equipment for triboelectric charge measurement
The structure of the equipment for the measurement of the triboelectric charge between a solid and a liquid is shown in Fig. 1. Figure 1(a) is the schematic diagram of the test system, and Fig. 1(b) is the optical image of the equipment. The equipment consists of three modules, i.e., motion control, measurement, and triboelectrification. The motion control module (the part in red color in Fig. 1(a)) includes a motor, an anti-static rope, and a sample holder. It can be used to realize the movement of the solid sample at different speeds. The measurement module (the part in green color in Fig. 1(a)) consists of a specially designed Faraday cup and an electrometer (Keithley, 6517B). The triboelectrification module (the part in blue color in Fig. 1(a)) is a liquid container, in which triboelectrification between the solid sample and the liquid is realized.

Measurement principle of Faraday cup
A Faraday cup consisting of an inner and an outer metallic cylinder is shown in Fig. 2.
When there exists a point charge inside the Faraday cup, under the electric field ( ) E  caused by the charge, there will be a potential difference (V 1 − V 2 ) between the inner and the outer cylinder, as shown in Fig. 2 The grounding of the outer cylinder is equivalent to electromagnetic shielding. In this case, the Faraday cup can be regarded as a cylindrical capacitor, and the theoretical calculation equation of the Faraday cup capacitance is expressed by Eq. (1): where C F is the capacitance of the Faraday cup, ε 0 (8.85×10 −12 C 2 /(N·m 2 )) is the permittivity of vacuum, and ε r is the relative permittivity of air, and its value is 1.00053 when neglecting the influence of temperature and humidity. R i and R o are the midline radii of the inner and the outer cylinders, respectively, and L is the height of the Faraday cup. The amount of charge (Q) can be calculated by Eq. (2): where V m is the potential difference between the inner and the outer cylinder measured by the electrometer when there is no leakage of electric field lines in the Faraday cup. For the charge measurement using a Faraday cup, the charge leakage through the openside is usually unavoidable and affects the accuracy of the measurement. Accurate evaluation and control of the charge leakage during the charge measurement are necessary for the study of the triboelectrification mechanism between a solid and a liquid. For a non-closure Faraday cup, the term leakage ratio is used to describe the charge leakage and can be calculated by Eq. (3): where r l is the leakage ratio of the Faraday cup, Φ e is the electric flux of the openings on both ends of the Faraday cup, Φ ic is the electric flux of the inner cylinder, S e is the sum of the areas of the two open ends, S s (S e + S ic , where S ic is the area of the inner cylinder) is the sum of the areas of the two open ends and the inner cylinder,  E is the electric field vector, and A  represents the area traversed by the electric field. Taking into account the charge leakage, Eq. (2) is modified as Finally, the amount of the charge is calculated according to the modified Eq. (4). It can be seen that after taking into account the leakage ratio (r l ), the calculated charge will be greater than the value without considering the leakage ratio (r l ), which is closer to the true value and makes the charge measurement more precise.

Simulation of the electrostatic field model
For a point charge in the Faraday cup, the spatial electric field distribution can be analytically obtained, and the charge leakage can be directly calculated. However, for a charged bulk with a certain shape, the analytical calculation becomes difficult, and numerical simulation is generally required. A method for Faraday cup leakage ratio evaluation was established based on the simulation of electrostatic field distribution. The parameters of the Faraday cup were then optimized based on the electrostatic field distribution simulation. An electrostatic field model was built up based on COMSOL Multiphysics software (COSMOL, version 5.6), and the geometrical model is shown in Fig. 3. In this model, a cuboid was chosen as the solid sample, and two metal cylinders were built up to act as the inner and outer cylinders of the Faraday cup. The charged solid sample was placed inside the Faraday  The sizes of the model used in the simulation are shown in Table 1, and the dimensions of the Faraday cup are marked in Fig. 3. The parameters of the samples and the Faraday cup are chosen according to the ranges used in the experiments. In consideration of symmetry, a spherical air domain is set as the simulation solution domain, which is a commonly used shape for simulation [37,38]. Considering that the maximum inner cylinder height is 1,080 mm (Table 1) where V is the scalar electric potential, which is dependent on the spatial position, and ρ is the surface charge density of the solid sample. The electric field and electric potential can be calculated with appropriate boundary conditions, which determine the electrical variables on the boundaries of the physical model. The default initial value of the potential of the Initial Values node is 0 V, and the Zero Charge node is added. Zero potential is applied to the Ground node.
The electric field distribution is determined based on Gauss's Law, and the electric potential is calculated by Eq. (5). The electric flux could be obtained by integrating the area of  E at the openings on both ends and the inner cylinder of the Faraday cup. Then the leakage ratio can be calculated by Eq. (3).
As shown in Fig. 4, the solution domain is constructed with free tetrahedral meshes, which describe the geometry of complex shapes and better describe the edges and corners. The infinite element layer is constructed with triangular prism elements.
Generally, the calculation accuracy is mainly affected by the meshing accuracy. The general principle of mesh division is that when the mesh is subdivided to a certain extent, the calculation result converges to an allowable error range; and when it is further subdivided, the simulation result does not change significantly. Figure 5 shows the variation of the calculated leakage ratio with the number of meshes. In the simulation, the following parameters were used: D i = 150 mm, i t H D r = 3, and the distance between the inner cylinder and the outer cylinder (D) is 15 mm. It can be seen from Fig. 5 that when the mesh number   For the electric field simulation, it is considered that the error meets the requirement of computation precision. Hence, 1.5 × 10 6 was set as the cut-off point of the mesh number.

Parameter optimization of the Faraday cup
To optimize the design of the Faraday cup, the leakage ratio (r l ) with different geometric parameters were calculated. The geometric parameters of the Faraday cup used for the calculation are shown in Table 1. Figure 6 shows a typical distribution of the electric field generated by a charged sample with ρ = −100 nC/m 2 . The parameters of the Faraday cup and the sample are as follows: L = 450 mm, D i = 150 mm, D = 15 mm, L S = 100 mm, and t s = 3 mm. The electric potential around the sample decreases rapidly with distance from the sample. Since the outer cylinder is grounded, the electric potential near the outer cylinder is zero. Figure 7 shows the variation of the r l with the    was investigated, and the results are shown in Fig. 9 when D i = 150 mm. It can be seen from Fig. 9 that the r l is significantly dependent on the is better to be larger than 3, and the leakage ratio is usually less than 5% in this case.
In addition, the size of the sample varies in specific measurements. To study the influence of the sample size on the r l , the r l for the charged samples with different L S was simulated, and the results are shown in Fig. 10. In Fig. 10

Apparatus and materials
Based on the simulation results, a Faraday cup with i t H D r = 3 was produced, and measurement equipment was developed. The specific geometric parameters of the designed Faraday cup are shown in Table 2, in which the capacitance value was measured by using an LCR digital bridge (Tonghui, TH2822E), and the r l was calculated based on the electrostatic field model in this work.
www.Springer.com/journal/40544 | Friction Charge measurements for triboelectrification between solids and liquids were performed to validate the feasibility of the method. The solid samples with the size of 100 mm × 100 mm × 3 mm were used in experiments. Insulating material PTFE and conductive material aluminum alloy 5010 (Al 5010) were used as the solid materials. Their contact angles (CAs) with DI water and sodium chloride (NaCl) solution with the concentration of 3.5% are shown in Table 3. To eliminate the initial charge on the sample surface, before experiment, the solid samples were firstly sonicated in ethanol for 20 min, secondly in DI water for 20 min, and then left in the air for 12 h. The liquids used in experiments are DI water (insulating) and NaCl solution (conductive). The specific properties of the solids and the liquids are shown in Table 4. Besides, six speeds of 4, 8, 12, 16, 20, and 24 mm/s were chosen to validate if the present equipment can be used to study the effect of speed on the triboelectrification between PTFE and DI water. During the experiments, temperature and relative humidity (RH) were maintained at 19-21 °C and 35%-45% RH, respectively.

Experimental validation
Charge measurement for triboelectrification between PTFE and DI water was performed. The experimental process (Fig. 11) includes two steps. In the first step, the sample was pulled from position 1 to position 3 and then to position 1, measuring the original charge on the surface of the solid sample. In the second step, the sample was pulled from position 1 to position 4 and then to position 1, performing the solid-liquid electrification process. The starting point of the solid sample position 1 is above the Faraday cup. In the second step, the solid sample goes down through the Faraday cup with a speed of 16 mm/s, and then enters the liquid until the entire sample is merged in the liquid. Then, the sample is pulled upward, passes through the Faraday cup, and returns to the starting point to complete a measurement cycle. Figure 11 shows the measurement process of triboelectrification between a PTFE sample and DI water, in which the variation of the measured voltage and the calculated charge by Eq. (7) are presented. Generally, there are original charges on the surface of the PTFE sample due to the functional groups, the dangling bonds, etc. [40], and they are hardly to be totally removed. When the charged sample approaches the Faraday cup (positions 1 to 2), it induces a potential difference between the inner and outer cylinders of the Faraday cup. The value of the induced negative potential gradually increases and reaches a maximum value and basically does not change when the sample is completely moved into the Faraday cup. The original surface charge of the  After the sample totally enters the liquid (positions 3 to 4) and comes out (positions 4 to 3), the Faraday cup measures the charge of the sample after the solidliquid charge transfer (positions 3 to 2 and 1). The charge transfer can be calculated by Eq. (7), in which V o and V t are the measured induced potential before and after solid-liquid charge transfer, respectively.
where Q t is the amount of charge transfer in the solidliquid triboelectrification process. The triboelectric charge density (σ t ) can thus be calculated by Eq. (8): where S is the contact area between the solid sample and liquid (surface area of the solid sample). Repeated experiments of triboelectrification between the PTFE and DI water were performed. The triboelectrification experiment curves of the three samples (PTFE1-DI water, PTFE2-DI water, and PTFE3-DI water) are shown in Fig. 12. Figure 12 shows the original curves of repeated experiments. It can be seen from Fig. 12(a) that the initial surface charge of PTFE samples are negative, and the corresponding values of initial charge density of surface (ρ 0 ) are also calculated and drawn in Fig. 12(b). Alternatively, The σ t and the average values of σ t of the three experiments are shown in Fig. 12(b). It can be found that the discreteness of the results is not significant within the range of −148.4 ± 12.61 nC/m 2 . The error among the three σ t may originate from the differences in the initial charge density of sample surfaces.
In order to validate the wider applicability of the method, experiments were performed for two typical solid materials (PTFE and Al 5010) and liquids (DI water and 3.5% NaCl solution), and the results are shown in Fig. 13. Figure 13(a) shows the triboelectric experiment curves of PTFE-DI water and PTFE-NaCl solution. Figure 13(b) shows the triboelectric experiment curves of Al 5010-DI water and Al 5010-NaCl solution. For each solid material and liquid, the experiments were repeated for three times. The average σ t and error bar are shown in Fig. 13(c). It can be seen from Fig. 13(c) that regardless of whether the liquid is conductive or not, the PTFE insulator produces a large charge transfer when PTFE rubbed against the liquid. While for the conductive material Al 5010, the result is different. The Al 5010 produces very weak charge transfer regardless of whether the liquid is conductive or not. Furthermore, it can be seen from Figs. 13(a) and 13(b) that the initial surface of PTFE is negatively charged, and the original surface of Al 5010 samples have very weak positive or negative charge. In Fig. 13, the Al 5010 sample, whose initial charge is positive, is abbreviated as Al-IP, and the Al 5010 sample negatively charged is abbreviated as Al-IN. During the process of solid-liquid triboelectrification, PTFE samples have a negative charge transfer by rubbing with DI water and NaCl solution, which is consistent with the results of Refs. [3,41]. For the triboelectrification experiments of Al 5010-DI water and Al 5010-NaCl solution, the initial charge of Al 5010 affects the polarity of triboelectric charge transfer; when the initial surface charge of Al 5010 is negative, the transfer charge is positive; and when the surface charge of Al 5010 is positive, the triboelectric transfer charge is negative.
www.Springer.com/journal/40544 | Friction For both hydrophobic and hydrophilic materials, there is more or less water molecule adsorption and residue after rubbing with liquids to study the influence of water residue on the measurement of triboelectric charge. For the two materials chosen in our validation experiments, PTFE (the CA with DI water is 113.4°) and Al 5010 (the CA with DI water is 83.0°), we measured the charge dissipation curve in the Faraday cup for 30 min after rubbing with DI water. The process is shown in Fig. 14. After the completion of the triboelectric process and charge measurement process above, the sample was pulled into the Faraday cup to record the curve of charge dissipation. The charge dissipation curves of PTFE and Al 5010 are shown in Fig. 14. It can be seen that the surface charge of PTFE and Al 5010 changes slightly after charge dissipation for 30 min. It indicates that for both of these two materials, although the adsorption and residue of water molecules on the surface will affect the triboelectric charge transfer, the effect is small compared to the actual amount of triboelectric charge transfer.

Triboelectrification experiments at different speeds
The experimental results of triboelectrification of PTFE and DI water at different speeds are shown in Fig. 15. It can be found that the triboelectric transfer charge densities show a general trend of increasing and then decreasing with the increasing speed. It is consistent with the trend in Ying et al. [42] and shows that the speed is a factor to influence the triboelectric performance of solid-liquid frictional system. However, since the focus of this work is to propose a precise method to measure the amount of solid-liquid triboelectric charge, detailed mechanism of the speed influence has not been discussed and will be further studied and discussed in the future work.

Conclusions
A method based on the Faraday cup has been developed to measure the charge transfer between solids and liquids. The leakage ratio of Faraday cup was determined by the simulation based on the electrostatic field model built in this work. By controlling the ratio of height to pitch diameter of the inner cylinder and the ratio of the distance between the inner and outer cylinder to pitch diameter of the inner cylinder, the accurate measurement of the charge can be achieved. An apparatus was developed, and the charge measurement method was validated by the experiments of triboelectrification between both conductive and non-conductive solids and liquids. The proposed method was proved to be feasible for measuring charge transfer at the solid-liquid interface.
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