Method and apparatus for measuring surface charge density and surface potential of a dielectric material

Abstract

This invention belongs to, but is not limited to, the field of surface analysis technology, and particularly relates to a method and apparatus for measuring the surface charge density and surface potential of dielectric materials, comprising: S1, applying an external electric field to subject the dielectric material to be measured to an electrostatic force F, which is transmitted to the pendulum frame through a sample holder; S2, the pendulum frame rotates by an angle Δθ under the action of the electrostatic force F; S3, the magnitude of the angle Δθ is equal to the displacement x of the intermediate plate of the bottom capacitor displacement detection system; S4, the differential capacitance ΔC of the two capacitors in the capacitor displacement detection system is proportional to the rotation angle Δθ; S5, after modulation and demodulation by the capacitance sensing circuit, ΔC is converted into a voltage output signal V. O .

Description

Technical Field

[0001] This invention belongs to, but is not limited to, the field of surface analysis technology, and particularly relates to a method and apparatus for measuring the surface charge density and surface potential of dielectric materials. Background Technology

[0002] Surface charge density is a crucial physical quantity describing the distribution of surface charge in materials, widely used in materials science, nanotechnology, electronic devices, and biosensors. Accurate measurement of surface charge density is essential for understanding the electrical properties of materials, surface interactions, and the behavior of biomolecules on surfaces. For example, in electrochemical reactions, the charge distribution on the electrode surface significantly affects reaction rates and selectivity. In biosensors, the binding capacity of biomolecules is often closely related to their surface charge density. Therefore, developing efficient and accurate surface charge density measurement techniques is particularly important. Currently, various methods for measuring surface charge density have been developed, including:

[0003] Kelvin probe force microscopy (KPFM) is a technique that combines atomic force microscopy with the Kelvin method. The basic principle of the Kelvin method (…) Figure 2 (As shown) the surface potential of a sample is measured using a probe with a known work function. Before the probe contacts the sample, both have the same vacuum energy level but different Fermi levels, resulting in different work functions. Upon contact, electrons migrate from the lower work function to the higher work function, thus leveling the Fermi level. This causes a change in the vacuum energy levels. The difference in vacuum energy levels is the contact potential difference (CPD) V. CPD = (Φ tip -Φ sample To obtain the specific value of the contact potential difference, a reverse voltage equal to the contact potential difference can be applied between the probe and the sample, thus aligning their vacuum energy levels. By measuring the DC voltage applied between the probe and the sample through the measuring circuit, a clear characteristic can be obtained showing the state when their vacuum energy levels are aligned, thereby obtaining the specific value. The work function of the probe is known, so the work function of the sample can be measured.

[0004] 1. Technological development

[0005] The Kelvin probe principle was first proposed by Lord Kelvin in 1898, primarily for measuring the contact potential difference between materials. This principle laid the foundation for later Kelvin probe force microscopy. First reported in 1991, researchers combined Kelvin probe technology with atomic force microscopy (AFM) to achieve nanoscale imaging of surface potentials, achieving significant results in areas such as surface charge distribution, charge transfer, and the work function of metallic materials. With the continuous development of nanotechnology and materials science, KPFM technology is also constantly advancing. Researchers are exploring higher-resolution measurement methods and new application areas; for example, KPFM has shown great potential in quantum computing and the development of novel electronic devices. However, it also has some drawbacks that affect its effectiveness and reliability in applications.

[0006] The working principle of a vibrating capacitance electrometer for measuring charge density mainly utilizes the compensation method, such as... Figure 1 As shown. The compensation method uses the vibration of an electret or an electrode containing an air gap at a certain frequency to create a corresponding alternating electric field in the air gap, replacing the measurement of the induced alternating current in the dynamic capacitor method. Specifically, the measurement principle involves applying a modulated anti-phase AC voltage to the air gap. This is used to compensate for the air gap electric field between the electret and the electrode, until the air gap electric field... The value is 0 (achieving complete compensation). Therefore, the equivalent surface charge density of the electret in a single-sided plated electrode is 0. for:

[0007]

[0008] This method is a non-contact measurement. Its basic advantage is that the charge density can be determined without measuring the air gap thickness.

[0009] 2. Practical Application

[0010] The compensation method is a non-contact method, and it is commonly used in the market by... Figure 2 The EST102 vibrating capacitance electrometer shown is shown.

[0011] Figure 2 The vibrating capacitance electrometer shown is priced at around RMB 22,000.

[0012] Based on the above analysis, the urgent technical problems that need to be solved in the existing technology are:

[0013] (1) Surface property dependence: The performance of Kelvin probe microscopes is highly dependent on the surface properties of the sample. Different surface conditions can lead to significant variations in measurement results, making it difficult to compare different samples. In addition, the cleanliness, roughness, and morphology of the sample can affect the measurement results, which requires the sample to be carefully prepared and processed before measurement.

[0014] (2) Sensitivity to the environment: Kelvin probe microscopes are highly sensitive to environmental conditions such as temperature, humidity, and electromagnetic interference. Small changes in the environment can affect the measurement results, so these variables must be carefully controlled during experiments. This high dependence on the environment may limit its applicability in some practical applications.

[0015] (3) Vibrating capacitance electrometers are not suitable for high-precision experiments and are expensive. Summary of the Invention

[0016] To address the problems existing in the prior art, the present invention provides a method and apparatus for measuring the surface charge density and surface potential of dielectric materials.

[0017] This invention is implemented as follows: a method for measuring the surface charge density and surface potential of a dielectric material, comprising:

[0018] S1, The applied electric field causes the dielectric material to be tested to be subjected to an electrostatic force F, which is transmitted to the pendulum frame through the sample holder;

[0019] S2, the angle of rotation of the pendulum frame under the action of electrostatic force F. ;

[0020] S3, angle The size is equal to the displacement of the intermediate plate of the bottom capacitor displacement detection system. ;

[0021] S4, the differential capacitance of the two capacitors in the capacitive displacement detection system. With rotation angle Proportional;

[0022] S5, after modulation and demodulation by the capacitive sensing circuit Converted into voltage output signal .

[0023] Furthermore, the equations of motion are:

[0024] (1)

[0025] Where I and θ are the moment of inertia and angular displacement of the pendulum, respectively; K is the stiffness; λ is the damping coefficient; τ is the applied torque; and F, L, and ω are the amplitude, arm length, and frequency of the electrostatic force, respectively. The pendulum swings at an angle θ under the action of the electrostatic force F. The tangential component of gravity, Mg sin θ, and the electrostatic force F together provide the acceleration of the pendulum. If the angle is very small, the tangential component of gravity can be approximately written as Mg... .

[0026] (2)

[0027] Where β = λ / (2I). The first term is the transient solution, where the frequency is... The initial phase is The initial amplitude is The second term is a frequency of The initial phase is ϕ, and the amplitude is The steady-state solution, here It can be represented as:

[0028] (3)

[0029] in It is the natural frequency of the pendulum, expressed as:

[0030] (4)

[0031] Furthermore, when the electrostatic force frequency ω→0, that is, when the electrostatic force is a constant force, we can obtain from equation (3):

[0032] (5)

[0033] Therefore, the electrostatic force on a compound pendulum is proportional to the angle of rotation of the pendulum.

[0034] S is the surface area of ​​the dielectric material to be tested. Let the total charge on its surface be denoted as: Then the surface charge density is expressed as:

[0035] (6)

[0036] Given that the potential difference applied to the electrode plates AB is U, and the distance between the electrode plates AB is D, the electrostatic force F on the dielectric material can be written as:

[0037] (7)

[0038] Surface charge density of dielectric materials It can be represented as

[0039] (8)

[0040] s is the thickness of the dielectric material to be tested. The relative permittivity of the dielectric material to be measured. Then the relationship between the surface charge density and surface potential of the dielectric material is:

[0041] (9)

[0042] Furthermore, from equations (5), (8), and (9), it can be seen that the surface charge density, surface potential, and electrostatic force experienced by the dielectric material under test are all related to the angle of rotation of the compound pendulum. Related. Regarding the angle of rotation of the compound pendulum. The measurement principle is as follows:

[0043] At the angle of rotation of the display stand When I was very young, , This refers to the displacement of the intermediate capacitor plate in the capacitance detection system placed at the bottom of the swing frame. The displacement of the intermediate plate will... The measurement uses a variable-gap capacitance detection method.

[0044] When the electrostatic force is zero, the distance between the middle plate and both the left outer plate A and the right outer plate B is d. When the electrostatic force is not zero, the middle plate undergoes displacement. The distance between the middle electrode plate and the left outer electrode plate A is The distance between the middle electrode plate and the right outer electrode plate B is The capacitance formed by the middle plate and the left plate A Increase the capacitance formed by the middle plate and the right outer plate B. Decrease, respectively:

[0045] (10)

[0046] (11)

[0047] Where A, d, and C0 represent the area of ​​the capacitor plates when they are directly aligned, the spacing between them, and the capacitance value under the condition of mass equilibrium. Let be the dielectric constant of air. Then the difference between these two capacitors can be expressed as:

[0048] (12)

[0049] when Since the value is very small, higher-order terms are ignored. Equation (12) becomes:

[0050] (13)

[0051] Detected differential capacitance signal After being modulated and demodulated by the capacitive sensing circuit, it is converted into a voltage output signal V.O V O Linear relationship:

[0052] (14)

[0053] Equations (5), (13), and (14) yield the electrostatic force F and the output voltage of the capacitance detection circuit. The relationship is:

[0054] (15)

[0055] This is the proportionality coefficient. Then, from equations (7), (9), and (15), the surface charge density of the material to be measured can be obtained. and surface potential Relationship with the output voltage of the capacitor detection circuit:

[0056] (16)

[0057] (17)

[0058] in and This is the proportionality coefficient.

[0059] Another object of the present invention is to provide a dielectric material surface charge density and surface potential measuring device for implementing the aforementioned method for measuring the surface charge density and surface potential of dielectric materials.

[0060] The system includes a pendulum frame, counterweight, clamps, electrode A, calibration bracket, sample, electrode B, sample holder, reed, counterweight, outer electrode B, outer electrode A, and capacitive displacement sensor. To ensure stability and meet installation requirements, the pendulum frame employs a U-shaped design, with a central crossbeam for mounting the counterweight and other components. The reed is fixed by upper and lower clamps; the upper clamp is fixed to a bracket inside the container, and the lower clamp is fixedly connected to the pendulum frame. The vertical orientation of the pendulum is adjusted by the counterweight, which also adjusts its stiffness. The calibration bracket is installed on the side of the pendulum frame, allowing for the placement of a known mass block to calibrate the pendulum's stiffness. The material to be tested is mounted on the central sample holder of the pendulum, with its force perpendicular to the frame. Electrodes A and B are connected to the positive and negative terminals of an external power supply and are placed on either side of the sample holder, providing an electric field to the sample. The angular displacement of the pendulum is monitored by a capacitive displacement sensor mounted at the bottom of the pendulum.

[0061] Furthermore, the construction of the device framework specifically includes:

[0062] The pendulum frame 1 adopts a U-shaped frame design, with a counterweight 2 installed in the middle of the frame to adjust its stability. Upper and lower clamps 3 on both sides of the frame fix the springs 9, and the center of gravity of the pendulum is adjusted by the counterweight 10. The springs 9 are fixed by the upper and lower clamps 3; the upper clamp is fixed to the support inside the container, and the lower clamp is fixedly connected to the pendulum frame. The calibration bracket 5 is installed on the bottom side of the pendulum frame. The capacitance displacement detection system 11-13 is installed below the pendulum frame to monitor the pendulum's displacement. The sample is fixed in the middle of the sample holder 8, and the electrode plates 4 and 7 are distributed independently on the left and right sides of the sample holder, separate from the pendulum frame. The assembled sample holder is then fixed below the frame. Finally, the positive and negative terminals of the voltage source are connected to the electrode plates to provide an electric field for the sample. The assembled pendulum device is carefully placed inside a stainless steel container to complete subsequent parameter calibration.

[0063] Furthermore, the calibration steps specifically include:

[0064] electrostatic force Surface charge density and surface potential The key to accurate measurement is obtaining the proportionality coefficient. This step is achieved by calibrating the compound pendulum device. After the compound pendulum device is assembled, the stiffness of the compound pendulum system is calibrated using the gravity moment method, which involves measuring... The basic idea of ​​the gravitational torque method is to use an object of known mass to generate a restoring torque on a compound pendulum, and to calibrate the system stiffness through this restoring torque. A standard object of mass m is placed on the pendulum frame, and its horizontal distance from the suspension point is l. The restoring torque generated by this object on the pendulum can be expressed as mgl. By loading and unloading the standard object onto the pendulum, the position of the pendulum will change. Based on the local gravitational acceleration g, the mass m of the standard object, its lever arm l, and the change in the angle of motion ∆θ of the compound pendulum, the following relationship can be obtained:

[0065] (18)

[0066] The torque of the electrostatic force F acting on the sample to be tested is L, which can be obtained from equation (5).

[0067] (19)

[0068] Equation (19) shows that Its effect is comparable to that of FL. By loading standard objects m of different masses, multiple sets of measurements are performed. The resulting output ,like Figure 7 As shown, it can be measured and The relationship, that is In reality, it is just... Therefore, we obtained the calibration coefficient using the known standard mass m through calibration methods. From equation (15), we can see that:

[0069] (20)

[0070] Finally, the surface charge density of the material to be tested can be obtained according to equations (16) and (17). and surface potential .

[0071] Furthermore, the calibration coefficients can be obtained according to the aforementioned calibration steps. Then, according to equation (17), the electrostatic force F and the output voltage can be obtained. The ratio coefficient between Place the dielectric material sample to be tested on the sample holder. Connect the positive and negative terminals of the voltage source to electrode plates A4 and B7. Close the stainless steel chamber door to prevent interference from air and electromagnetic waves. Turn on the voltage source and observe the output voltage of the capacitance detection circuit using an oscilloscope. Finally, the surface charge density of the material to be tested can be obtained according to equations (16), (17), and (20). and surface potential .

[0072] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the method for measuring the surface charge density and surface potential of the dielectric material.

[0073] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the method for measuring the surface charge density and surface potential of the dielectric material.

[0074] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0075] First, this invention places the sample to be tested on a pendulum sample holder, which is simultaneously placed in an applied electric field. The surface charge density / surface potential of the sample is measured by measuring the rotation angle of the pendulum. A higher surface charge density / surface potential corresponds to a greater electrostatic force on the pendulum, resulting in a larger rotation angle. The rotation angle is converted into an output voltage by a capacitance detection circuit. The output voltage of the capacitance detection circuit is proportional to the rotation angle, which in turn is proportional to the electrostatic force on the pendulum, and consequently, to the surface charge density / surface potential of the sample. The stiffness of the pendulum holder is primarily provided by gravity and can be adjusted by changing the center of mass. Using gravity to directly calibrate the holder eliminates interference from other force couplings. When the pendulum system stiffness is set to approximately 1 Nm / rad, the electrostatic force measurement range reaches 1000 μN with a measurement accuracy of 0.09 μN, corresponding to a surface potential measurement range of 0-10000 V for dielectric materials with a measurement accuracy of 0.09 V. Therefore, the advantages of this invention are: (1) it has an ultra-wide measurement range of surface potential, and (2) it has ultra-high measurement accuracy of surface potential within the wide measurement range.

[0076] Secondly, the technical solution of this invention solves a long-standing but unresolved technical problem: in surface measurement technology, current methods mainly rely on Kelvin probes and vibrating capacitance electrometers. Both have drawbacks affecting their effectiveness and reliability in application. This invention places the sample to be tested on a pendulum sample holder, which is simultaneously placed in an external electric field. The surface charge density / surface potential of the sample is measured by measuring the rotation angle of the pendulum. A higher surface charge density / surface potential corresponds to a greater electrostatic force on the pendulum, resulting in a larger rotation angle. The rotation angle is converted into an output voltage by a capacitance detection circuit. This output voltage is proportional to the rotation angle, which in turn is proportional to the electrostatic force on the pendulum, and consequently, to the surface charge density / surface potential. The stiffness of the pendulum holder is primarily provided by gravity and can be adjusted by changing the center of mass. Directly calibrating the holder using gravity eliminates interference from other force couplings. When the stiffness of the pendulum system is set to about 1 Nm / rad, the electrostatic force measurement range reaches 1000 μN and the measurement accuracy reaches 0.09 μN. The corresponding measurement range of the surface potential of the dielectric material is 0-10000 V and the measurement accuracy reaches 0.09 V. Therefore, the advantages of this invention are: (1) it has an ultra-wide measurement range of surface potential, and (2) it has ultra-high measurement accuracy of surface potential within the wide measurement range.

[0077] Third, the technical solution of this invention solves the problems of inaccurate, unstable, and slow response speed in the measurement of surface charge density and surface potential of dielectric materials in existing technologies. Existing technologies often rely on traditional charge measurement methods, which may be affected by environmental noise and other interferences, resulting in inaccurate measurement results. This invention, through a compound pendulum frame and a differential capacitance displacement detection system, can measure charge density and surface potential at a higher resolution, avoiding the signal instability problem caused by weak electrostatic forces in traditional methods.

[0078] The significant technological advancements of this invention are as follows: First, its design, based on the linkage between the compound pendulum frame and electrostatic force, effectively amplifies the minute charge reactions of the dielectric material under test in an electric field, resulting in a significant improvement in measurement sensitivity. Second, the use of a differential capacitance displacement detection system enables high-precision detection of minute changes in the rotation angle of the compound pendulum, effectively reducing interference from environmental factors and thus obtaining more accurate measurement results. Furthermore, the modulation and demodulation technology of the capacitance sensing circuit converts the differential capacitance signal into a stable voltage output signal, further improving the system's response speed and signal stability.

[0079] Therefore, the technical solution of this invention has strong practicality and advancement in industrial applications, providing an innovative solution for high-precision measurement of the surface electrical properties of dielectric materials, and promoting technological progress in materials science, electronic engineering and related fields. Attached Figure Description

[0080] Figure 1 This is a schematic diagram illustrating the principle of measuring surface charge density using a vibrating capacitance electrometer.

[0081] Figure 2 This is a schematic diagram illustrating the working principle of the Kelvin probe microscope provided in this embodiment of the invention;

[0082] Figure 3 This is a schematic diagram of the electrostatic force acting on the sample under test in an electric field, provided in an embodiment of the present invention.

[0083] Figure 4 This is a schematic diagram of the variable-gap capacitor detection principle provided in an embodiment of the present invention;

[0084] Figure 5 This is a schematic diagram of the capacitance sensing circuit provided in an embodiment of the present invention;

[0085] Figure 6 This is a logic block diagram provided in an embodiment of the present invention;

[0086] Figure 7 This is a schematic diagram of the gravity calibration unit provided in an embodiment of the present invention;

[0087] Figure 8 This is a structural diagram of the compound pendulum measuring frame provided in an embodiment of the present invention;

[0088] Figure 9 This is a graph showing the electrostatic force and applied voltage experienced by a polytetrafluoroethylene (PTFE) thin film after electret deposition.

[0089] In the diagram: 1. Pendulum frame, 2. Counterweight, 3. Clamp, 4. Electrode A, 5. Calibration bracket, 6. Sample, 7. Electrode B, 8. Sample bracket, 9. Spring, 10. Counterweight, 11. Intermediate electrode, 12. Outer electrode A, 13. Outer electrode B. Detailed Implementation

[0090] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0091] The device provided by this invention is used to measure the surface charge density and surface potential of dielectric materials, and its working principle is as follows:

[0092] 1. Electrostatic force: In step S1, an external electric field is applied to the sample 6 to be tested through plates A4 and B7, generating an electrostatic force F. This force is transmitted to the pendulum frame 1 of the compound pendulum through the sample holder 8, causing the pendulum frame to rotate.

[0093] 2. Pendulum rotation: The electrostatic force F causes the pendulum frame 1 to rotate around a fixed point, resulting in an angular change Δθ. This angular change is proportional to the surface charge density of sample 6; the higher the surface charge density, the stronger the electrostatic force, and the larger the resulting rotation angle Δθ.

[0094] 3. Displacement Detection: The rotation of the pendulum frame 1 causes displacement of the intermediate electrode plate 11 at its bottom relative to the outer electrode plates A12 and B13. The capacitive displacement sensor detects the displacement change of the intermediate electrode plate 11, reflecting the angular change Δθ of the pendulum frame.

[0095] 4. Signal Processing: The capacitive displacement sensor converts the detected displacement change into a differential capacitance signal ΔC. Through modulation and demodulation by the capacitive sensing circuit, the differential capacitance signal ΔC is converted into a voltage output signal VO. After calibration, the magnitude of VO directly represents the surface charge density and surface potential of sample 6, realizing the measurement of the electrical properties of the dielectric material.

[0096] The method for measuring the surface charge density and surface potential of dielectric materials provided by this invention is based on the pendulum motion under electrostatic force and the differential capacitance principle of a capacitance displacement detection system. First, in step S1, an applied electric field generates an electrostatic force F on the dielectric material to be tested. This electrostatic force is transmitted to the pendulum frame through the sample holder, generating a force. This force is caused by the reaction of the surface charge of the dielectric material under the applied electric field, resulting in a change in its surface potential.

[0097] In step S2, the electrostatic force F causes the pendulum frame to rotate by a certain angle ∆. This angle ∆ This represents the effect of electrostatic force on the compound pendulum system and is an important parameter for measuring the surface charge density of the dielectric material under test. Angle ∆ The magnitude of the electrostatic force F is directly proportional to the surface charge density. In other words, the higher the surface charge density, the greater the electrostatic force generated, resulting in a larger rotation angle.

[0098] Next, in step S3, the angle ∆ The size and displacement of the intermediate plate in the bottom capacitor displacement detection system Equal. This displacement Corresponding to the rotation angle, it reflects the displacement change of the compound pendulum system. Displacement The magnitude of the potential is also determined by the surface charge density, so it directly reflects the change in surface potential of the dielectric material being tested.

[0099] Finally, in steps S4 and S5, the two capacitors in the capacitive displacement detection system form a differential capacitor, and the differential capacitor ∆C is related to the rotation angle ∆. Proportional. After modulation and demodulation by the capacitance sensing circuit, the differential capacitance signal ∆C is converted into a voltage output signal V. O V O The size of the value can be directly represented by the surface charge density and surface potential of the dielectric material through calibration, thus realizing the measurement of the electrical properties of the dielectric material.

[0100] The compound pendulum testing system mainly includes a pendulum frame, counterweight, clamps, electrode A, calibration bracket, sample, electrode B, sample holder, reed, counterweight, outer electrode B, outer electrode A, and capacitive displacement sensor. To ensure the stability of the pendulum frame and meet installation requirements, a U-shaped frame design is adopted, with the central crossbeam used to mount the counterweight and other components. The reed is fixed by upper and lower clamps; the upper clamp is fixed to the bracket inside the container, and the lower clamp is fixedly connected to the pendulum frame. The vertical attitude of the pendulum is adjusted by the counterweight on the pendulum frame, and the stiffness of the pendulum is also adjusted by the counterweight. The calibration bracket is installed on the side of the pendulum frame, and a mass block of known mass can be placed on the calibration bracket to calibrate the stiffness of the pendulum. The material to be tested is installed on the central sample holder of the pendulum, with its force perpendicular to the frame. Electrodes A and B are connected to the positive and negative terminals of an external power supply and are placed on both sides of the sample holder, providing an electric field to the sample under test when the power is turned on. The angular displacement of the pendulum is monitored by a capacitive displacement sensor installed at the bottom of the pendulum.

[0101] Its measurement principle allows us to consider the pendulum frame as a compound pendulum. It is a typical second-order system, with the following equation of motion:

[0102] (1)

[0103] Where I and θ are the moment of inertia and angular displacement of the pendulum, respectively; K is the stiffness; λ is the damping coefficient; τ is the applied torque; and F, L, and ω are the amplitude, arm, and frequency of the electrostatic force, respectively. The pendulum oscillates at an angle θ under the action of the electrostatic force F, and the tangential component of gravity... Together with the electrostatic force F, it provides acceleration to the pendulum. If the angle is very small, the tangential component of gravity can be approximately written as Mg. .

[0104] (2)

[0105] Where β = λ / (2I). The first term is the transient solution, where the frequency is... The initial phase is The initial amplitude is The second term is a frequency of The initial phase is ϕ, and the amplitude is The steady-state solution, here It can be represented as:

[0106] (3)

[0107] in It is the natural frequency of the pendulum, expressed as:

[0108] (4)

[0109] When the frequency of the electrostatic force ω→0, that is, when the electrostatic force is a constant force, we can obtain from equation (3):

[0110] (5)

[0111] Therefore, the electrostatic force on a compound pendulum is proportional to the angle of rotation of the pendulum.

[0112] On the other hand, the dielectric material under test is subjected to electrostatic forces in the electric field of electrode plate AB, such as... Figure 3 As shown

[0113] S is the surface area of ​​the dielectric material to be tested. Let the total charge on its surface be denoted as: Then the surface charge density is expressed as:

[0114] (6)

[0115] Given that the potential difference applied to the electrode plates AB is U, and the distance between the electrode plates AB is D, the electrostatic force F on the dielectric material can be written as:

[0116] (7)

[0117] Surface charge density of dielectric materials It can be represented as

[0118] (8)

[0119] s is the thickness of the dielectric material to be tested. The relative permittivity of the dielectric material to be measured. Then the relationship between the surface charge density and surface potential of the dielectric material is:

[0120] (9)

[0121] Therefore, from equations (5), (8), and (9), it can be seen that the surface charge density, surface potential, and electrostatic force of the dielectric material under test are all related to the angle of rotation of the compound pendulum. Related. Regarding the angle of rotation of the compound pendulum. The measurement principle is as follows:

[0122] At the angle of rotation of the display stand When I was very young, , This refers to the displacement of the intermediate capacitor plate in the capacitance detection system placed at the bottom of the swing frame. The displacement of the intermediate plate will... The measurement utilizes a variable-gap capacitance detection method, the principle of which is as follows: Figure 5 As shown.

[0123] When the electrostatic force is zero, the distance between the middle plate and both the left outer plate A and the right outer plate B is d. When the electrostatic force is not zero, the middle plate undergoes displacement. The distance between the middle electrode plate and the left outer electrode plate A is The distance between the middle electrode plate and the right outer electrode plate B is The capacitance formed by the middle plate and the left plate A Increase the capacitance formed by the middle plate and the right outer plate B. Decrease, respectively:

[0124] (10)

[0125] (11)

[0126] Where A, d, and C0 represent the area of ​​the capacitor plates when they are directly aligned, the spacing between them, and the capacitance value under the condition of mass equilibrium. Let be the dielectric constant of air. Then the difference between these two capacitors can be expressed as:

[0127] (12)

[0128] when Since the value is very small, higher-order terms are ignored. Equation (12) becomes:

[0129] (13)

[0130] Detected differential capacitance signal Through capacitive sensing circuit (such as) Figure 5 (As shown) After modulation and demodulation, it is converted into a voltage output signal V. O V O Linear relationship:

[0131] (14)

[0132] The main principles and logic of the entire patent are as follows: Figure 6 As shown:

[0133] According to the logic box Figure 6 From equations (5), (13), and (14), we can obtain the electrostatic force F and the output voltage of the capacitance detection circuit. The relationship is:

[0134] (15)

[0135] This is the proportionality coefficient. Then, from equations (7), (9), and (15), the surface charge density of the material to be measured can be obtained. and surface potential Relationship with the output voltage of the capacitor detection circuit:

[0136] (16)

[0137] (17)

[0138] in and This is the proportionality coefficient.

[0139] I. Constructing the Device Frame

[0140] The pendulum frame 1 adopts a U-shaped frame design, with a counterweight 2 installed in the middle of the frame to adjust its stability. Upper and lower clamps 3 on both sides of the frame fix the springs 9, and the center of gravity of the pendulum is adjusted by the counterweight 10. The springs 9 are fixed by the upper and lower clamps 3; the upper clamp is fixed to the support inside the container, and the lower clamp is fixedly connected to the pendulum frame. The calibration bracket 5 is installed on the bottom side of the pendulum frame. The capacitance displacement detection system 11-13 is installed below the pendulum frame to monitor the pendulum's displacement. The sample is fixed in the middle of the sample holder 8, and the electrode plates 4 and 7 are distributed independently on the left and right sides of the sample holder, separate from the pendulum frame. The assembled sample holder is then fixed below the frame. Finally, the positive and negative terminals of the voltage source are connected to the electrode plates to provide an electric field for the sample. The assembled pendulum device is carefully placed inside a stainless steel container to complete subsequent parameter calibration.

[0141] II. Calibration Steps

[0142] electrostatic force Surface charge density and surface potential The key to accurate measurement is obtaining the proportionality coefficient. This step is achieved by calibrating the compound pendulum device. After the compound pendulum device is assembled, the stiffness of the compound pendulum system is calibrated using the gravity moment method, which involves measuring... The basic idea of ​​the gravitational torque method is to use an object of known mass to generate a restoring torque on a compound pendulum, and to calibrate the system stiffness through this restoring torque. If a standard object of mass m is placed on the pendulum frame, and its horizontal distance from the suspension point is l, then the restoring torque generated by this object on the pendulum can be expressed as... By loading and unloading a standard object onto the pendulum, the pendulum's position changes. Based on the local gravitational acceleration g, the mass m of the standard object, its lever arm l, and the change in the pendulum's angle of motion ∆θ, the following relationship can be obtained:

[0143] (18)

[0144] On the other hand, the torque of the electrostatic force F acting on the sample to be tested is L, which can be obtained from equation (5).

[0145] (19)

[0146] show Its effect is comparable to that of FL. By loading standard objects m of different masses, multiple sets of measurements are performed. The resulting output It can be calculated and The relationship, that is In reality, it is just... Therefore, the calibration coefficient was obtained using the known standard mass m through calibration. From equation (15), we can see that:

[0147] (20)

[0148] Finally, the surface charge density of the material to be tested can be obtained according to equations (16) and (17). and surface potential .

[0149] III. Measurement of Surface Potential

[0150] The calibration coefficients can be obtained based on the aforementioned calibration steps. Then, according to equation (17), the electrostatic force F and the output voltage can be obtained. The ratio coefficient between Place the dielectric material sample to be tested on the sample holder. Connect the positive and negative terminals of the voltage source to electrode plates A4 and B7. Close the stainless steel chamber door to prevent interference from air and electromagnetic waves. Turn on the voltage source and observe the output voltage of the capacitance detection circuit using an oscilloscope. Finally, the surface charge density of the material to be tested can be obtained according to equations (16), (17), and (20). and surface potential .

[0151] An application embodiment of the present invention provides a computer device, which includes a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of a method for measuring the surface charge density and surface potential of a dielectric material.

[0152] An application embodiment of the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of a method for measuring the surface charge density and surface potential of a dielectric material.

[0153] This invention can be specifically applied to the following fields:

[0154] 1. Energy Storage: - Capacitors and Supercapacitors: In energy storage devices, the surface charge characteristics of the dielectric material directly affect its storage capacity and efficiency. By measuring its surface potential and charge distribution, the design of the capacitor can be optimized to improve energy density and discharge efficiency.

[0155] 2. Electronic Devices: - Semiconductor Device Performance Optimization: In the semiconductor field, the distribution of surface charge has a significant impact on the electrical performance of devices. By measuring the surface potential of dielectric materials, we can gain a deeper understanding of interface characteristics, thereby improving the performance of devices such as transistors and diodes.

[0156] 3. Sensor Technology: - Developing Novel Sensors: Based on the surface charge properties of dielectric materials, highly sensitive sensors can be developed. These sensors can be used to detect gases, chemicals, and biomolecules, and are widely used in environmental monitoring, medical diagnostics, and other fields.

[0157] 4. Energy Conversion: Applications of Triboelectric Materials: In the research of triboelectric materials, the visualization and quantification of surface charge are crucial. By measuring the surface charge of these materials, their properties can be effectively tuned, promoting applications in energy conversion and energy harvesting.

[0158] 5. Materials Science: - Materials Characterization and Development: In the field of materials science, the measurement of surface charge density can provide important information for the development of new materials. By understanding the behavior of different materials under an electric field, materials with specific electrical properties can be developed, promoting the application of new materials.

[0159] 6. Nanotechnology: - Nanomaterials and Devices: In nanotechnology, methods for measuring surface charge are crucial for understanding the electrical properties of nanomaterials. This can be used to develop novel nanodevices, such as nanosensors and nanobatteries, thus advancing the application of nanotechnology.

[0160] like Figure 9 The figure shown is a data graph of the electrostatic force and applied voltage experienced by a polytetrafluoroethylene film after electret deposition using the technology of this invention.

[0161] In the description of this invention, unless otherwise stated, "a plurality of" means two or more; the terms "upper," "lower," "left," "right," "inner," "outer," "front end," "rear end," "head," "tail," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," "third," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0162] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0163] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for measuring the surface charge density and surface potential of a dielectric material, characterized in that, include: S1, The applied electric field causes the dielectric material to be tested to be subjected to an electrostatic force F, which is transmitted to the pendulum frame through the sample holder; S2, the angle of rotation of the pendulum frame under the action of electrostatic force F. ; S3, angle The size is equal to the displacement of the intermediate plate of the bottom capacitor displacement detection system. ; S4, the differential capacitance of the two capacitors in the capacitive displacement detection system. With rotation angle Proportional; S5, after modulation and demodulation by the capacitive sensing circuit Converted into voltage output signal ; The equation of motion is: （1） Where I and θ are the moment of inertia and angular displacement of the pendulum, respectively; K is the stiffness; λ is the damping coefficient; τ is the applied torque; F, L, and ω are the amplitude, arm, and frequency of the electrostatic force, respectively; the pendulum swings at an angle θ under the action of the electrostatic force F, and the tangential component of gravity is... Together with the electrostatic force F, they provide acceleration for the pendulum; If the angle is very small, the tangential component of gravity can be approximately written as Mg. ; （2） Where β = λ / (2I); the first term is the transient solution, where the frequency is... The initial phase is The initial amplitude is The second term is a frequency of The initial phase is ϕ, and the amplitude is The steady-state solution, here Represented as: （3） in It is the natural frequency of the pendulum, expressed as: （4）； When the frequency of the electrostatic force ω→0, that is, when the electrostatic force is a constant force, we can obtain from equation (3): （5） Therefore, the electrostatic force on a compound pendulum is directly proportional to the angle of rotation of the pendulum; S is the surface area of ​​the dielectric material to be tested. Let the total charge on its surface be denoted as: Then the surface charge density is expressed as: (6) Given that the potential difference applied to the electrode plates AB is U, and the distance between the electrode plates AB is D, the electrostatic force F on the dielectric material can be written as: (7) Surface charge density of dielectric materials It can be represented as (8) s is the thickness of the dielectric material to be tested. The relative permittivity of the dielectric material to be measured; then the relationship between the surface charge density and surface potential of the dielectric material is: (9)； From equations (5), (8), and (9), it can be seen that the surface charge density, surface potential, and electrostatic force of the dielectric material under test are all related to the angle of rotation of the compound pendulum. Related; the angle of rotation of the compound pendulum The measurement principle is as follows: At the angle of rotation of the display stand When I was very young, , The displacement of the intermediate capacitor plate of the capacitance detection system placed at the bottom of the swing frame; The displacement of the intermediate plate will The measurement uses a variable-gap capacitance detection method; When the electrostatic force is 0, the distance between the middle plate and the left outer plate A and the right outer plate B is d. When the electrostatic force is not zero, the intermediate plate will be displaced. The distance between the middle electrode plate and the left outer electrode plate A is The distance between the middle electrode plate and the right outer electrode plate B is The capacitance formed by the middle plate and the left plate A Increase the capacitance formed by the middle plate and the right outer plate B. Decrease, respectively: （10） （11） Where A, d, and C0 represent the area of ​​the capacitor plates when they are directly aligned, the spacing between them, and the capacitance value under the condition of mass equilibrium. Let be the dielectric constant of air; then the difference between these two capacitors can be expressed as: (12) when When the value is small, higher-order terms are ignored; equation (12) becomes: (13) Detected differential capacitance signal After being modulated and demodulated by the capacitive sensing circuit, it is converted into a voltage output signal V. O V O Linear relationship: (14) Equations (5), (13), and (14) yield the electrostatic force F and the output voltage of the capacitance detection circuit. The relationship is: （15） The proportionality coefficient is used; the surface charge density of the material to be tested can then be obtained from equations (7), (9), and (15). and surface potential Relationship with the output voltage of the capacitor detection circuit: (16) (17) in and This is the proportionality coefficient; The calibration steps specifically include: electrostatic force Surface charge density and surface potential The key to accurate measurement is obtaining the proportionality coefficient. This step is achieved by calibrating the compound pendulum device. After the compound pendulum device is assembled, the stiffness of the compound pendulum system is calibrated using the gravity moment method, which is to measure... ; The basic idea of ​​the gravitational torque method is to use an object of known mass to generate a restoring torque on a compound pendulum, and to calibrate the system stiffness through this restoring torque. A standard object of mass m is placed on the pendulum frame, with a horizontal distance l from the suspension point. The restoring torque generated by this object on the pendulum is expressed as mgl. By loading and unloading the standard object onto the pendulum, the position of the pendulum will change. Based on the local gravitational acceleration g, the mass m of the standard object, its lever arm l, and the change in the angle of motion ∆θ of the compound pendulum, the following relationship can be obtained: (18) The torque of the electrostatic force F acting on the sample to be tested is L, which can be obtained from equation (5). (19) show It has a similar effect to FL; by loading standard objects m of different masses, multiple sets of measurements are performed. The resulting output It can be calculated and The relationship, that is In fact, it is From equation (15), we can see that: (20) Finally, the surface charge density of the material to be tested can be obtained according to equations (16) and (17). and surface potential .

2. A device for measuring the surface charge density and surface potential of dielectric materials, implementing the method for measuring the surface charge density and surface potential of dielectric materials as described in claim 1, characterized in that, The system includes a pendulum frame, counterweight, clamps, electrode A, calibration bracket, sample, electrode B, sample holder, reed, counterweight, outer electrode B, outer electrode A, and capacitive displacement sensor. To ensure stability and meet installation requirements, the pendulum frame employs a U-shaped design, with a central crossbeam for mounting the counterweight and other components. The reed is fixed by upper and lower clamps; the upper clamp is fixed to a bracket inside the container, and the lower clamp is fixedly connected to the pendulum frame. The vertical orientation of the pendulum is adjusted by the counterweight, which also adjusts its stiffness. The calibration bracket is installed on the side of the pendulum frame, allowing for the placement of a known mass block to calibrate the pendulum's stiffness. The test material is mounted on the central sample holder of the pendulum, with its force perpendicular to the frame. Electrodes A and B are connected to the positive and negative terminals of an external power supply, placed on either side of the sample holder, providing an electric field to the test sample. The angular displacement of the pendulum is monitored by a capacitive displacement sensor mounted at the bottom of the pendulum.

3. The device for measuring the surface charge density and surface potential of dielectric materials as described in claim 2, characterized in that, The specific components of the installation framework include: The pendulum uses a U-shaped frame design, with a counterweight installed in the middle of the frame to adjust its stability. Upper and lower clamps on both sides of the frame secure the springs, and the counterweight adjusts the pendulum's center of gravity. The springs are fixed by upper and lower clamps; the upper clamp is fixed to a support inside the container, and the lower clamp is fixedly connected to the pendulum. A calibration bracket is installed on the bottom side of the pendulum. A capacitance displacement detection system is installed below the pendulum to monitor its displacement. The sample is fixed in the middle of the sample holder, and electrode plates are fixed on the left and right sides of the holder. The assembled sample holder is then fixed below the frame. Finally, the positive and negative terminals of a voltage source are connected to the electrode plates to provide an electric field for the sample. The assembled pendulum device is carefully placed inside a stainless steel container to complete subsequent parameter calibration.

4. The device for measuring the surface charge density and surface potential of dielectric materials as described in claim 3, characterized in that, The calibration coefficients can be obtained based on the aforementioned calibration steps. Then, according to equation (17), the electrostatic force F and the output voltage can be obtained. The ratio coefficient between Place the dielectric material sample to be tested on the sample holder; connect the positive and negative terminals of the voltage source to electrode plates A4 and B7, close the stainless steel chamber door to prevent interference from air and electromagnetic waves, turn on the voltage source, and observe the output voltage of the capacitance detection circuit with an oscilloscope. Finally, the surface charge density of the material to be tested can be obtained according to equations (16), (17), and (20). and surface potential .

5. A computer device comprising a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the method for measuring the surface charge density and surface potential of a dielectric material as described in claim 1.

6. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the method for measuring the surface charge density and surface potential of a dielectric material as described in claim 1.

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