Influence of shape effect on dynamic surface charge transport mechanism of cellular electret after corona discharge

Jiawei ZHANG (張嘉偉), Zelei ZHANG (張澤磊), T MATSUMOTO,Qingqing GAO(高青青),Yuanye LIU(劉原野),K NISHIJIMA and Yifan LIU(劉亦凡)

1 School of Electrical Engineering, Xi’an University of Technology, Xi’an 710048, People’s Republic of China

2Faculty of Engineering, Fukuoka University, Fukuoka 814-0180, Japan

3Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China

Abstract Surface charge accumulation and transport on cellular polypropylene play an important role in nanogenerators,which could have a potential impact on energy harvesting and wearable devices for zero carbon energy systems and the internet of things.Different shapes have different charge accumulation and decay characteristics of the polymer.Therefore,we studied the influence of the sample’s shape on the surface charge decay by experiment and modeling.The surface potential of square and circular cellular polypropylene was measured by a two-dimensional surface potential measurement system with electrostatic capacitive probe.The experimental result shows that the surface potential distribution of the square sample dissipates non-uniformly from the bell shape to a one-sided collapsed shape,while that of the circular sample dissipates uniformly from the bell shape to the crater-like shape.Moreover, the simulated results of the initial surface potential distributions of the square and circular cellular polypropylene are consistent with the experimental results.The investigation demonstrates that the charge transport process is correlated with the shape of the sample, which provides significant reference for designing electret material used for highly efficient nanogenerators.

Keywords: charge transport, nanogenerator, corona discharge, simulation, shape effect, cellular polypropylene, sustainable energy

1.Introduction

Confronting the rapid development of the Internet of Things(IoT),the demand for wearable devices used for communication between humans and smart devices has surged.There is an urgent requirement to realize a sustainable power supply for wearable devices [1, 2].At present, nanogenerators, converting small and irregular energy in nature into electricity [3], are regarded as one of the effective methods for the power supply of wearable devices due to their low cost and high efficiency [4].Nanogenerators include triboelectric nanogenerators [5, 6],piezoelectric nanogenerators [7], and electrostatic induction generators[8],all of which generate power by the movement of inducing charge between the electrodes [9].The generation of electric charges can be attributed to the friction between materials and the energy conversion properties of the materials.Meanwhile, corona discharge is also one of the sources to generate electric charges.In order to improve the efficiency of the nanogenerator, it is significant to explore the characteristics of charge accumulation and decay of polymer materials in a nanogenerator.As one of the polymer materials, polypropylene can store the charge for a long time, which helps to better observe the charge transport characteristics.Therefore, in this work, cellular polypropylene has been chosen as the sample to study the transport mechanism of the surface charge.

Generally, there are three methods for measuring the surface/interface charge, including the dust map technique,optical measurement method based on Pockels effect,and the electrostatic capacitive probe method [10-12].Among them,the most widely used method is the electrostatic capacitive probe method.In the late 1960s, Davies first proposed the method of an electrostatic capacitive probe to measure the surface charge [13].Some previous investigations on surface charge measurement by electrostatic capacitive probe methods measured a point or scanned a line[14-16],which cannot comprehensively reflect the charge transport characteristics.Thus, we use a two-dimensional scanning platform based on the electrostatic capacitive probe method, which can comprehensively obtain the surface potential distribution map of materials after corona discharge.

Over the years, many investigations studied the charge transport characteristics of the insulating materials.In Kindersberger’s work [17, 18], the surface potential decay characteristics of three cylindrical insulator samples, including polytetrafluoroethylene (PTFE), silicone rubber (SIR)and epoxy resin (EP), were studied by the electrostatic capacitive probe method.In Mu’s work [19], the surface discharge phenomena of three square materials, including polyvinylidene fluoride,polyimide and polyethylene terephthalate films with different thicknesses, were studied by the optical measurement method based on Pockels effect.In Matsumoto’s work [20], the charge characteristics of the two cylindrical acrylic and glass epoxy multilayer discs after corona discharge were studied by the electrostatic capacitive probe method.The charge decay characteristics of different samples with the same shape were studied in detail, but the influence of the sample with different shapes on charge transport characteristics obtained little attention.

In this work,we used a two-dimensional scanning platform based on the electrostatic capacitive probe method,which can be used to measure the surface potential at different time instants of cellular polypropylene with different shapes after corona discharge.In addition, a simulation modeling of the initial surface potential after corona discharge has been established to build the relationship between the space electric field distribution and the charged functional dielectrics.The work provides an important reference for improving the efficiency of nanogenerators.

2.Experiment of surface charge accumulation and evacuation

2.1.Cellular electrets with various shape

The experiments were performed on commercially used cellular polypropylene with two different shapes: the 50 μm-thick circular sample had a diameter d = 200 mm,and the 50 μm-thick square sample had a side length l = 71 mm.

Before corona discharge, samples were strictly deionized and dried.The experiments were performed in ambient air with a temperature of 21.5 °C and a relative humidity of 25%.

2.2.Experimental setup of sample polarization and surface potential mapping

As shown in figure 1, the corona discharge system was composed of a needle-to-plate electrode and a DC power source,which was used to inject charge into the surface of the sample.The plate electrode was connected to the ground.The needle electrode was located directly above the sample with a distance of 2 cm and the radius of the tip of the needle electrode is 0.15 cm.

The system for measuring surface potential is shown in figure 2, which is composed of an electrostatic voltmeter(Trek 542-A),an electrostatic capacitive probe,a computer,a cross table and a grounded electrode.The surface potential data were acquired by voltmeter and monitored by the computer.In order to guarantee the accuracy of the experiment,the electrostatic capacitive probe was located above the sample with a distance of 10 mm.

The overall surface charge distribution map was achieved by an electrostatic capacitive probe mounted on a cross table that was controlled by the computer.Coordinates of the scanned point on the sample and its corresponding surface potential values can be obtained through the cross table scanning platform and the electrostatic voltmeter,respectively.The completion of a scanning process took 12 min for each sample.

Besides, a hygrometer was employed to record the temperature and relative humidity during the surface charge decay process.

2.3.Discharge parameters and surface potential measuring procedure

The cellular polypropylene sample placed on the grounded plate electrode was charged by the needle electrode with the applied voltage V = 15 kV and charging time of 5 min.After corona discharge, the grounded plate electrode and the sample were immediately moved to the two-dimensional surface potential measurement system.Then, the cross table started to scan preselected points on the surface of the sample.The scanning process was executed at different time instants after corona discharge to observe the accurate surface potential decay tendency over a long period.

2.4.Modeling of initial surface potential distribution based on finite element method

A model of corona discharge, developed and implemented by the finite element method, can be used to calculate the distribution of space potential within the discharge region including the potential of the upper surface of the sample.The model is composed of an anode needle electrode,a cellular polypropylene film, a grounded copper electrode and a discharge region.The needle electrode is located above the polypropylene film with a distance of 2 cm and the radius of the tip of the needle electrode is 0.15 cm.The 50μm-thick polypropylene film with the dielectric constant of 1.2 is placed on a grounded copper electrode.

In the model,the pressure and gas temperature are set to 1 atm and 21.5 °C, respectively.The mean value of the electron-positive ion recombination rate constant is 5 × 10?8cm3s?1, and the ion-ion recombination rate constant is considered as 2 × 10?6(T/300)?1.5cm3s?1, where T is the temperature of neutral species [21].

2.4.1.Governing equations.A corona discharge model is developed based on finite element method.The electron transport equation, multicomponent diffusion transport equation of the heavy species in the discharge process, the momentum balance equation, and Poisson’s equation for electric potential are taken into consideration [22].

The equations for the electron density are expressed as:

Wherenedenotes the electron density;Γeis the electron density flux;μeis the electron mobility which is either a scalar or tensor; E is the electric field;Deis electron diffusivity which is either a scalar or a tensor;uis the neutral fluid velocity;ε0is the vacuum permittivity;εris the relativepermittivity;ρqis the space charge density;Reis the electron rate expression; V is the potential.

Table 1.Simplified chemical reactions in air corona discharge.

The equations for the multicomponent diffusion equations are given by:

Here,jkis the diffusive flux vector;Rkis the rate expression for speciesk;uis the mass averaged fluid velocity vector;ρdenotes the density of the mixture;wkis the mass fraction of the kth species;Vkis the multicomponent diffusion velocity for speciesk;Dk,mis the mixture averaged diffusion coefficient;Mnis the mean molar mass of the mixture;T is the gas temperature;DkTis the thermal diffusion coefficient for speciesk;zkis the charge number for speciesk;μk,mis the mixture averaged mobility for speciesk; E is the electric field.

2.4.2.Boundary conditions

2.4.2.1.The wall boundary condition.

WhereΓeis the electron density flux;reis the reflection coefficient(usually 0);ve,this the thermal velocity;nedenotes the electron density;γiis the secondary emission coefficient from the ith positive ion;Γiis the ion flux of the ith positive ion at the wall;Γtis the thermal emission flux; →nis the normal vector.

The thermal velocity is expressed as:

Wherekbis the Boltzmann constant;Teis the electron temperature [23];meis the mass of the electron.

2.4.2.2.The boundary condition of the dielectric surface.The boundary conditions for the dielectric surface are expressed as[23]:

Table 2.Non-uniform surface potential distribution in different quadrants.

In the model of corona discharge,the simplified chemical reactions are shown in table 1,where A,P,n,e denote neutral particles, positive ions, negative ions, and electrons, respectively [24].

3.Results

3.1.Square sample

Figure 3 shows the surface potential distribution of the square sample at 0 h,3 h and 6 h after corona discharge.As shown in figure 3(a), the surface potential distribution at the initial moment shows a bell shape and the amplitude of surface potential gradually decreases from the center to the edge of the sample.The surface charge of the sample shows an overall decay tendency with the increase of time.The surface potential at the center point decreases from 4.637 to 4.126 kV within 6 h after corona discharge.In addition, it should be noted that, in figure 3(c), the surface potential distribution shows a slight collapse on one side.A tendency of non-uniform potential distribution could be observed.

Figure 1.Schematic of corona discharge system.

Figure 2.Schematic of surface potential measurement system.

Figure 3.Surface potential distribution of square sample ((a)0 h, (b)3 h, (c)6 h).

Figure 4.Surface potential distribution of square sample ((a)24 h, (b)48 h, (c)72 h).

As shown in figure 4, the surface charge decay becomes uneven after 24 h, the value of the surface potential of the fourth quadrant of the sample is considerably lower than that of the other quadrants, and the potential in the second quadrant shows the highest value.An obvious phenomenon of non-uniform potential distribution could be observed.The peak values of the potential in the first, the second and the third quadrants are summarized in table 2.

3.2.Circular sample

Figure 5 shows the surface potential distribution of the circular sample at different time instants after corona discharge.The surface potential distribution at the initial moment shows a bell shape, which is also observed in [20, 25, 26].At the initial moment, the amplitude of surface potential gradually decreases from the center to the edge of the sample.With the increase of time, these charges are not overall dissipated, but the dissipating speed of the charge at the center point is significantly faster than those at surrounding points close to the center point, which makes the bell shape gradually become a crater-like shape.The decay rate of the surface charge of the circular sample is considerably slower than that of the square sample.Moreover, the potential distribution of the circular sample in each stage is more uniform compared with the square one.

Figure 5.Surface potential distribution of circular sample ((a)0 h, (b)3 h, (c)6 h, (d)24 h, (e)48 h, (f)72 h).

Figure 6.Comparison of initial surface potential between simulation and experiment of the square sample.

Figure 7.Comparison of initial surface potential between simulation and experiment of the circular sample.

Figure 8.Charge transport paths of different samples.

4.Discussion

The topological disorder and chemical disorder in polymer materials lead to the formation of localized states (Anderson)in insulating materials [27].Charge carriers are captured by the trap, and the trapped charge will stay in the trap of the insulating material until enough energy is obtained to escape from the trap.Generally speaking, the residence time of the trapped charge is a positive exponential to the depth of the trap [28, 29].The residence time of carriers in the localized state may differ more than ten orders of magnitude [30].The charge trapping and detrapping weaken the migration rate of carriers, resulting in the accumulation of the charge on the surface of the sample.In addition, the injection of charges occurs on the surface of the dielectric.Therefore,whether it is a positive or negative charge, the traps are supposed to be filled from the deepest levels upwards[29].For higher surface potential, the deep traps are almost filled.As a result, the surface potential is highest at the center of the insulating material because the deep trap at the center of the material is more easily filled due to continuous charge injection.

Figure 6 shows that the simulated result of the distribution of surface potential on the square sample is consistent with the measured results at the initial stage.Figure 7 exhibits that the simulated result of the distribution of surface potential on circular sample is consistent with the measured results at 0-5 cm, but there are a few deviations at 5-10 cm, which could be attributed to the decrease of charge mobility caused by the trap formed by the disordered structure of the material.In addition, when the material was moved under the probe after discharge,the charge on the material surface can diffuse partially along with the bulk and the surface, which may be the cause of the error.

Figure 9.The changes of chemical bond in polypropylene film caused by corona discharge.

The surface charge transport is influenced by three mechanisms,which are lateral motion of the charge along the surface, released through the volume of the insulator and neutralized with the ions in the air [17, 18].Surface charge dissipation through air neutralization is attributed to the ion density of the ambient air [31].

The surface potential distribution of the square sample gradually dissipates from the bell shape to the one-sided collapsed shape, which could be due to the lateral diffusion of the charge.Charge spreading along the surface of the polymer often causes slight decay because the edge of the dielectric has deep traps which can prevent the charge from reaching the grounded electrode [26].From the surface potential distribution shown in figures 4 and 5,there is no build-up phenomenon at the edge of the sample.As schematically shown in figure 8,the non-uniform distribution of the transport path on the square sample results in the non-uniform resistance distribution path of the square sample.Then, the non-uniform resistance distribution path of the square sample will further lead to the non-uniform decay phenomenon of the deposited charge.Moreover, the escape of charge could form a pathway to accelerate the decay of the charge remaining on the surface of the square sample.Finally,the collapse of the surface potential map could be caused by an unbalanced charge density gradient and non-uniform electric field distribution.Therefore, the square sample gradually dissipates from the bell shape to the one-sided collapsed shape.Meanwhile, for the circular sample, a uniform transport path results in the uniform resistance distribution,which further forms a uniform decay phenomenon and makes the charge density gradient on the circular sample more balanced compared with the square one.Therefore, a uniform decay phenomenon of surface potential can be observed on the circular sample.Based on the above analysis, it can be demonstrated that the charge decay process is affected by the shape of the sample.

Besides, corona discharge can usually lead to the non-uniform modification on the surface of samples.The insulation property at the center of the sample could be modified more easily because the discharge electrode was located directly above the sample’s center.The non-uniform modification on the surface of samples also could affect the charge dissipation.Specifically, the plasma generated by corona discharge contains a large number of active high-energy particles.The energy of these particles can break the C-C bond and C-H bond in the polypropylene film when they bombard the surface of the material,which introduces oxygen-containing functional groups into the polypropylene molecular chain[32].The formations of the O radicals and the carbonyl groups make the surface charge trap become shallower, change the surface composition of the material,and improve the surface conductivity[33].Meanwhile,low-kinetic energy particles can also increase the surface conductivity of the material [34].The surface charge is easier to dissipate along the surface due to the increase of surface conductivity.In addition, these high-energy particles have an etching effect on the surface of insulating materials,which increases the surface roughness of insulating materials.The appropriate increase of the surface roughness also can accelerate the charge dissipation [33].

The surface potential distribution of the circular sample slowly dissipates from the bell shape to the crater-like shape,which is caused by the neutralization of gas ions and the change of the micro-resistance of the insulating material.Specifically,because the surface potential at the center is the highest and the field strength is the largest,only gas ions generated in a volume with a sufficiently high electric field can neutralize the surface charge.Most of the ions collected in the effective neutralization region are driven by the electric field force to an area with a larger charge density in the surface of the material.When the charges in the area are almost completely neutralized, the ions from the gas can be guided to the remaining edge until all the charges are neutralized [18, 20].Moreover, before corona discharge, the conductivity of the material is uniform.Figure 9 shows that the surface of the insulating material is damaged due to the chemical bond breaking at the gas-solid interface after corona discharge, which can lead to the reduction of the breakdown strength of the material and the increase of the dielectric loss and conductivity[35,36].The value of conductivity reaches the largest at the center position,and this value decreases gradually toward the edge of the material.The change in conductivity makes it easier for charges at the center position to dissipate.

The surface charge of the circular sample decays considerably slower than that of the square sample,which can be attributed to both the size and the decay paths.

5.Conclusion

The present investigation has shown the vital role of the sample’s shape on the charge transport process at the surface of polymer materials.In this work, the influence of the polypropylene with different shapes on the surface charge decay is explored by experiment and modeling.The experimental results show that the sample’s shape can lead to a non-uniform surface charge decay.Moreover, it is also demonstrated that the threedimensional distribution map of surface potential can comprehensively reflect the characteristics of surface charge accumulation and decay.In addition,for the modeling,the initial values of the simulated results are consistent with the experimental measurement, which could be used to establish the relationship between the space potential distribution and the initial surface potential of the sample after corona discharge.

It can be found that the influence of the sample’s shape on the surface charge decay is of great significance to the structural design of the nanogenerators.Meanwhile, it also provides an important reference for improving the efficiency of nanogenerators and the anti-electrostatic ability of insulation components in the electrical equipment, as well as electronic devices.

Acknowledgments

This work was supported by National Natural Science Foundation of China(NSFC)(Nos.52050410346,51877031,62061136009),the Ministry of Science and Technology(No.QNJ2021041001), the high-level talents plan of Shaanxi province, the ‘Belt and Road Initiative’ Overseas Expertise Introduction Center for Smart Energy and Reliability of Transmission and Distribution Equipment of Shaanxi Province, and the Advanced Foreign Researcher Promotion Program of Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT)and Fukuoka University.In addition, we thank Mr Y Izawa for his suggestions and help in the experiment.