Silicon dioxide hollow sphere with MOF composite layer, manufacturing method and dielectric loss prediction method

Abstract

The invention relates to the technical field of silicon dioxide surface modification, in particular to a silicon dioxide hollow sphere with an MOF composite layer, a manufacturing method and a dielectric loss prediction method. The silicon dioxide hollow sphere comprises a hollow spherical structure formed by silicon dioxide, an amino silane layer grafted on the surface of an inner core layer through a covalent bond, a ZIF-8 crystal layer growing in situ by taking amino as a nucleation site, and thiol groups distributed on the outer surface of an MOF crystal. According to the silicon dioxide hollow sphere with the MOF composite layer, the manufacturing method and the dielectric loss prediction method, the silicon dioxide hollow sphere with the MOF composite layer has good compatibility and stability in an LCP matrix, the dielectric loss is small, and the performance of a high-frequency FPC is effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of silica surface modification, and particularly relates to a silica hollow sphere with an MOF composite layer, a manufacturing method, and a dielectric loss prediction method. Background Art

[0002] Currently, there are key problems in the liquid crystal polymer (LCP) composite materials in high-frequency flexible printed circuit boards (FPCs) before and after hydrothermal aging, such as poor dielectric properties, low bonding strength with copper foil, high coating technical requirements, and insufficient technical data for substrate integrated waveguide (SIW) design.

[0003] Silica hollow spheres have received increasing attention in recent years due to their excellent physical and chemical properties and broad application prospects. They exhibit good performance in fields such as catalysis, drug delivery, and adsorption materials. Studies have shown that they can be applied in the structure of high-frequency FPCs to improve performance. However, there are still some problems with existing silica hollow spheres in practical applications, mainly reflected in the simplicity of their surface properties and insufficient functionalization: Conventional silica hollow spheres usually only have hydroxyl groups on their surfaces, lacking other functional groups, resulting in the simplicity of the functions of silica hollow spheres in the LCP matrix, poor interfacial stability, and lack of molecular selectivity, which affects the performance of high-frequency FPCs. Summary of the Invention

[0004] In order to overcome the disadvantages and deficiencies existing in the prior art, the purpose of the present invention is to provide a silica hollow sphere with an MOF composite layer, a manufacturing method, and a dielectric loss prediction method. The silica hollow sphere with this composite layer has good compatibility and stability in the LCP matrix, and has less dielectric loss, effectively improving the performance of high-frequency FPCs.

[0005] The present invention is achieved through the following technical solutions: In the first aspect, the present invention discloses a silica hollow sphere with an MOF composite layer, which includes: Inner core layer: a hollow spherical structure composed of silica, with an average particle size of 200 - 800 nm, a wall thickness of 20 - 50 nm, and a specific surface area ≥ 350 m² / g; Bridging layer: an amino silane layer grafted onto the surface of the inner core layer through covalent bonds, with an amino density of 2.5 - 3.2 per nm² and a layer thickness of 1 - 3 nm; MOF crystal layer: a ZIF-8 crystal layer grown in-situ with amino groups as nucleation sites, with a thickness of 50 - 150 nm, a crystal size of 20 - 50 nm, and a pore diameter of 3.3 - 3.5 Å; Functionalized surface layer: thiol groups distributed on the outer surface of the MOF crystals, with a sulfur element content of 0.5 - 2 wt%, and satisfying the following structural relationship:

[0006] Among them, is the density of thiol groups, is the density of amino groups.

[0007] Combined with the first aspect, further, the proportion of the cavity volume of the core layer , and the hydroxyl density is 4.8 - 5.2 per nm²; The silane molecules of the amino-silane layer are in an upright orientation, and the molecular tilt angle measured by ellipsometry is ≤15°; The thiol groups are located at the edges of the MOF crystals.

[0008] In the second aspect, the present invention discloses a method for fabricating silica hollow spheres, which includes the following steps: S100. Pretreat the silica hollow spheres to activate the surface hydroxyl groups; S200. Perform amination modification on the activated silica hollow spheres with a γ-aminopropyltriethoxysilane solution to obtain amino-functionalized silica; S300. Using the amino group as the nucleation site, in-situ grow a ZIF-8 crystal layer in a methanol solution of zinc salt and 2-methylimidazole; S400. React the product obtained in step S300 with a thioacetamide solution to perform surface thiolation modification.

[0009] Combined with the second aspect, further, in step S200, the concentration of the γ-aminopropyltriethoxysilane solution is 3 - 8 wt%, the reaction pH value is 4 - 6, the reaction temperature is 60 - 80 °C, and the reaction time is 4 - 8 hours.

[0010] Combined with the second aspect, further, in step S300, the zinc salt is zinc nitrate, the zinc ion concentration is 0.05 - 0.2 M, the 2-methylimidazole concentration is 0.3 - 0.6 M, the reaction temperature is 30 - 40 °C, and the reaction time is 8 - 24 hours.

[0011] Combined with the second aspect, further, in step S400, the concentration of the thioacetamide solution is 0.3 - 0.8 M, the reaction temperature is 50 - 70 °C, the reaction time is 2 - 6 hours, and the sulfur element content of the obtained product is 0.5 - 2 wt%.

[0012] In the third aspect, the present invention discloses a method for predicting the dielectric loss of silica hollow spheres, which is characterized by including the following steps: a. Calculate the interfacial binding energy density through molecular dynamics simulation :

[0013] Among them, is the repulsive term coefficient of the Lennard-Jones potential, is the attractive term coefficient of the Lennard-Jones potential, is the hydrogen bond interaction strength coefficient, is the attenuation coefficient of the hydrogen bond interaction, is the minimum interatomic interaction distance, is the stage radius; b. Establish a three-dimensional electric field distribution equation based on the finite element method:

[0014]

[0015]

[0016] Among them, is the position-dependent relative permittivity, is the electric potential distribution function, is the interface polarization point and density, is the vacuum permittivity, effective charge quantity, is the number of interface dipoles per unit volume, is the reciprocal of the Boltzmann factor, is the interface binding strength parameter, is the absolute temperature; c. Construct the complex permittivity frequency domain response function:

[0017] Among them, is the high-frequency baseline permittivity, is the change in permittivity contributed by interface polarization, is the angular frequency, is the relaxation time, is the Cole-Cole distribution parameter, is the direct current conductivity; d. Obtain the total dielectric loss through vector superposition:

[0018]

[0019]

[0020]

[0021]

[0022] Among them, is the volume fraction weight factor, is the interfacial bonding strength weight, is the activation energy correlation weight, is the dispersion correction term, is the norm of the dielectric constant gradient, is the distribution uniformity index.

[0023] Combined with the third aspect, further, the interfacial bonding strength parameter is defined as:

[0024] Among them, is the number of atomic pairs for statistics, is the change in atomic pair spacing, is the partial derivative of the interfacial energy with respect to the atomic spacing.

[0025] Combined with the third aspect, further, in step c, by measuring the relaxation time at different temperatures, the activation energy is fitted out, The extraction method of the activation energy is:

[0026] Among them, is the pre-exponential factor, is the reference temperature, is the Boltzmann constant.

[0027] Combined with the third aspect, further, in step d, the calculation formula of the distribution uniformity index is:

[0028] Among them, is the th position coordinate of the filler particle, is the average value of the filler positions, is the standard deviation of the positions.

[0029] Advantages of the present invention: A silica hollow sphere with an MOF composite layer, a manufacturing method and a dielectric loss prediction method of the present invention not only improve the structural stability through the integration of adsorption-catalysis dual functions, but also make the dielectric anisotropy index and the dielectric constant lower due to the MOF composite layer orientation growth technology, effectively improving the performance of high-frequency FPC. Description of the drawings

[0030] The present invention will be further described with reference to the accompanying drawings. However, the embodiments in the drawings do not constitute any limitation to the present invention. For those of ordinary skill in the art, other drawings can be obtained based on the following drawings without creative efforts.

[0031] Figure 1 This is a method for fabricating silica hollow spheres in an embodiment of the present invention. Detailed implementation manners

[0032] To make the above objects, features, and advantages of the present invention more apparent and understandable, the following detailed description of the specific implementation manners of the present invention will be given with reference to the accompanying drawings. Many specific details are set forth in the following description to fully understand the present invention. However, the present invention can be implemented in many other ways different from those described herein. Those skilled in the art can make similar improvements without departing from the connotation of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed below.

[0033] Currently, there are key problems in the high-frequency flexible printed circuit board (FPC), such as poor dielectric properties, low bonding strength with copper foil, high coating technical requirements, and insufficient design technical data for substrate integrated waveguide (SIW) before and after the hydrothermal aging of liquid crystal polymer (LCP) composites.

[0034] Silica hollow spheres have received increasing attention in recent years due to their excellent physical and chemical properties and broad application prospects. They exhibit good performance in fields such as catalysis, drug delivery, and adsorption materials. Research shows that they can be applied in the structure of high-frequency FPCs to improve performance. However, there are still some problems in the actual application of existing silica hollow spheres, mainly reflected in the simplicity of their surface properties and insufficient functionalization: The surface of traditional silica hollow spheres usually only has hydroxyl groups and lacks other functional groups, resulting in poor dispersion state and dispersion stability of silica hollow spheres in the LCP matrix, affecting the performance of high-frequency FPCs.

[0035] To solve the above problems, this embodiment discloses a silica hollow sphere with a MOF composite layer, which includes: Inner core layer: A hollow spherical structure composed of silica, with an average particle size of 200 - 800 nm, a wall thickness of 20 - 50 nm, and a specific surface area ≥ 350 m² / g; Bridging layer: An amino silane layer grafted onto the surface of the inner core layer through covalent bonds, with an amino density of 2.5 - 3.2 per nm² and a layer thickness of 1 - 3 nm; MOF crystal layer: A ZIF-8 crystal layer grown in-situ with amino groups as nucleation sites, with a thickness of 50 - 150 nm, a crystal size of 20 - 50 nm, and a pore size of 3.3 - 3.5 Å; Functionalized surface layer: Thiol groups are distributed on the outer surface of the MOF crystal, with a sulfur element content of 0.5-2 wt%, and satisfy the following structural relationship:

[0036] wherein, is the thiol group density, is the amino group density.

[0037] Furthermore, the cavity volume ratio of the inner core layer , providing a nano-reactor for the catalytic reaction; the hydroxyl density is 4.8-5.2 per nm² to ensure effective grafting of the silane coupling agent; The silane molecules in the amino-silane layer are in an upright orientation, and the molecular tilt angle measured by ellipsometry is ≤15°; The thiol groups are located at the edges of the MOF crystal, and the sulfur retention rate is ≥85% in the pH range of 3-10.

[0038] In one embodiment, relevant performance tests are conducted on the silica hollow spheres: 1. Adsorption performance Test conditions: Pb²⁺ / Cd²⁺ / Cu²⁺ mixed solution (each 100 ppm, pH = 6) Results:

[0039] 2. Catalytic performance Reaction system: 4-nitrophenol (0.1 mM) + NaBH4 (10 mM), loaded with 1.2 wt% Au nanoparticles Results:

[0040] 3. Dielectric performance Test frequency band: 28 GHz (5G millimeter-wave communication frequency band) Results:

[0041] As Figure 1 shown, furthermore, this embodiment also discloses a method for fabricating silica hollow spheres, which includes the following steps: S100. Pretreat the silica hollow spheres to activate the surface hydroxyl groups; S200. Aminate the activated silica hollow spheres with a γ-aminopropyltriethoxysilane solution to obtain amino-functionalized silica; S300. Using the amino group as the nucleation site, in-situ grow a ZIF-8 crystal layer in a methanol solution of zinc salt and 2-methylimidazole; S400. React the product obtained in step S300 with a thioacetamide solution to perform surface thiolation modification.

[0042] In this embodiment, the amino group layer provides basic adsorption sites to capture cations, and the adsorption performance is increased by at least 2.1 times; the ZIF-8 crystal layer has a pore size of 3.4 Å for screening small-sized ions, and the selectivity coefficient reaches 8.5:1; the -SH in the thiol layer forms strong coordination bonds with heavy metals, and the adsorption capacity is further increased by 45%.

[0043] Furthermore, in step S200, the concentration of the γ-aminopropyltriethoxysilane solution is 3-8 wt%, and the concentration range ensures that the monolayer grafting coverage rate is between 0.7 and 0.9, avoiding defects in the MOF layer caused by multi-layer stacking; the reaction pH value is 4-6, so that the ratio of the hydrolysis rate to the condensation rate of KH550 is between 1.2 and 1.8, avoiding the formation of bulk gel; the reaction temperature is 60-80 °C, and the reaction time is 4-8 hours. The reaction temperature makes the terminal amino group of the silane molecule orient outwards (contact angle < 15°), improving the availability of MOF nucleation sites.

[0044] Furthermore, in step S300, the zinc salt is zinc nitrate, and the zinc ion concentration is 0.05-0.2 M, so that the nucleation rate is maintained within ; the concentration of 2-methylimidazole is 0.3-0.6 M, regulating the anisotropy index of crystal growth and promoting the preferential growth of crystal planes; the reaction temperature is 30-40 °C, and the reaction time is 8-24 hours to reduce the grain boundary energy.

[0045] Combined with the second aspect, furthermore, in step S400, the concentration of the thioacetamide solution is 0.3-0.8 M, the reaction temperature is 50-70 °C, the reaction time is 2-6 hours, and the sulfur element content of the obtained product is 0.5-2 wt%.

[0046] In a third aspect, the present invention discloses a method for predicting the dielectric loss of silica hollow spheres, which is characterized by including the following steps: a. Calculate the interfacial binding energy density through molecular dynamics simulation :

[0047] Among them, is the repulsive term coefficient of the Lennard-Jones potential, which is determined by the atomic repulsion, and its dimension is , reflecting the short-range repulsion between in the MOF and the benzene ring of LCP, avoiding excessive penetration of the molecular chain; is the attractive term coefficient of the Lennard-Jones potential, which is determined by the van der Waals attraction, and its dimension is , representing the strength of the stacking effect, directly affects the interfacial binding energy; is the strength coefficient of hydrogen bond interaction, and its dimension is , quantifying the contribution of hydrogen bonds to the interfacial energy. The larger the value, the stronger the interfacial chemical bonding; is the attenuation coefficient of hydrogen bond interaction, and its dimension is , controlling the range of hydrogen bond interaction. The larger the D value, the more localized the hydrogen bond interaction; is the minimum interatomic interaction distance, and its dimension is nm, avoiding non-physical situations of atomic overlap in calculations; is the stage radius, and its dimension is nm, balancing the calculation accuracy and efficiency. Usually, the distance at which the force decays to 1% is taken; Specifically, the above steps achieve the quantification of the stacking and hydrogen bond synergistic effects between the MOF layer and the LCP chain, with a calculation error of 5% technical effect.

[0048] b. Establish a three-dimensional electric field distribution equation based on the finite element method:

[0049]

[0050]

[0051] Among them, is the position-dependent relative permittivity, determined by the filler distribution and interfacial properties, reflecting the non-uniformity of the electric field distribution in the composite material, and directly affecting the local field strength; is the electric potential distribution function, used to calculate the electric field strength, and its dimension is V, evaluating the risk of dielectric breakdown; is the interfacial polarization point and density, generated by dipole orientation and interfacial bound charges, and its dimension is , quantifying the contribution of interfacial polarization to dielectric loss, and is positively correlated with the density of surface functional groups of the filler; is the vacuum permittivity, and its dimension is , used for normalization calculation; The effective charge quantity, related to the polarity of the interfacial chemical bond, and its dimension is C, reflecting the degree of charge transfer between the -SH group and the LCP. The larger the value, the stronger the interfacial dipole moment; is the number of interfacial dipoles per unit volume, and its dimension is , which is jointly determined by the porosity of the MOF layer and the filling degree of the LCP segments; is the reciprocal of the Boltzmann factor, and its dimension is , correlating the regulatory effect of temperature on the distribution of polarization charges; Specifically, the above steps reveal the mechanism of electric field distortion at the filler-matrix interface and predict the local field strength distribution.

[0052] c. Construct the frequency-domain response function of the complex permittivity:

[0053] Use the fractional derivative to describe the interfacial polarization relaxation , solving the problem of the failure of the Cole-Cole model in the high-frequency band; Among them, is the high-frequency baseline permittivity, reflecting the contribution of electronic polarization, characterizing the polarization ability of the material in the optical frequency band, and is related to the intrinsic polarity of LCP; is the relaxation strength, corresponding to the change in permittivity contributed by interfacial polarization. The larger the value, the more significant the influence of interfacial polarization on the dielectric properties; is the angular frequency, whose dimension is rad / s, a direct characterization of the working frequency, and determines the response rate of the polarization mechanism; is the relaxation time, whose dimension is s, and the activation energy The larger it is, the slower the relaxation; is the Cole-Cole distribution parameter. The stronger the interfacial binding, the more uniform the relaxation; is the direct current conductivity, characterizing the ohmic loss caused by ion migration, whose dimension is S / m, affected by the proton conduction of -SH groups on the filler surface. If the value is too large, it will increase the dielectric loss; Specifically, the above steps accurately characterize the dielectric relaxation behavior in the 10 - 40 GHz frequency band, and the goodness of fit R²≥0.98.

[0054] d. Obtain the total dielectric loss through vector superposition:

[0055]

[0056]

[0057]

[0058]

[0059] Among them, is the volume fraction weight factor, is the interface bonding strength weight, is the activation energy correlation weight, is the dispersion correction term, is the distribution uniformity index; is the norm of the dielectric constant gradient, characterizing the intensity of the electric field distortion, and its dimension is , and the larger the value, the more serious the non-uniformity of the local field strength, resulting in space charge accumulation loss; Specifically, the prediction error of the above steps in the 28 GHz frequency band is ≤7%, meeting the design requirements of 5G millimeter wave materials.

[0060] Dispersion correction term reflects the non-linear effect of filler agglomeration on electric field distortion.

[0061] The above steps can be achieved through a four-step progressive modeling and multi-physics field coupling algorithm: Microscopic controllability: Nano-scale parameters such as interface binding energy and crystal orientation are directly correlated with macroscopic dielectric properties; High-frequency accuracy: The prediction error in the 28 GHz millimeter wave frequency band is <6%, far exceeding the international peer level.

[0062] Strong universality: It has been successfully applied to the development of 6 types of high-frequency electronic devices such as 5G radomes and radar absorbing materials.

[0063] By constructing a multi-scale dielectric loss prediction model, the three major technical bottlenecks existing in traditional empirical models in the high-frequency band (5G millimeter wave band), namely insufficient accuracy, lack of microscopic structure correlation, and neglect of multi-physics field coupling, are solved, and quantitative and accurate prediction from microscopic interface characteristics to macroscopic dielectric properties is realized.

[0064] Combined with the third aspect, further, the definition formula of the interface bonding strength parameter is:

[0065] Among them, is the statistical number of atomic pairs, taking the atomic pairs within 1 nm³ of the contact interface between MOF and LCP to ensure statistical significance; is the change in atomic pair spacing, and its dimension is nm, reflecting the dynamic fluctuation of the interface. The smaller the value, the more stable the interface bonding; is the partial derivative of the interface energy with respect to the atomic spacing, and its dimension is eV / nm, characterizing the gradient of the interatomic force. The larger the value, the higher the interface bonding stiffness.

[0066] Combined with the third aspect, further, in step c, by measuring the relaxation time at different temperatures , the activation energy is fitted , Activation energy is extracted in the following way:

[0067] wherein, is the pre-exponential factor, whose dimension is s and is related to the intrinsic polarization rate of the material; is the reference temperature, whose dimension is K and is used to normalize the influence of temperature on the relaxation time; is the Boltzmann constant, whose dimension is eV / K and is used to establish the conversion relationship between thermal energy and activation energy.

[0068] Combined with the third aspect, further, in step d, the distribution uniformity index is calculated as follows:

[0069] wherein, is the position coordinate of the th filler particle, which is obtained by digital processing of the SEM image, and the resolution needs to reach 0.1 μm / pixel; is the average value of the filler positions. Ideally, should be close to the geometric center of the sample; is the standard deviation of the positions, indicating the improvement of the dispersion uniformity; the dimensions of the above parameters are all μm.

[0070] By clearly defining the key parameters in the dielectric loss prediction model and their measurement methods, the two major problems of unreliable models and incomparable results caused by fuzzy parameters and inconsistent measurement standards in traditional technologies are solved, providing a standardized and reproducible technical basis for dielectric property prediction.

[0071] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than limiting the protection scope of the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the essence and scope of the technical solutions of the present invention.

Claims

1. A silica hollow sphere with a MOF composite layer, characterized in that, Including: Core layer: A hollow spherical structure composed of silica, with an average particle size of 200 - 800 nm, a wall thickness of 20 - 50 nm, and a specific surface area ≥ 350 m² / g; Bridging layer: An amino - silane layer grafted onto the surface of the core layer through covalent bonds, with an amino density of 2.5 - 3.2 per nm² and a layer thickness of 1 - 3 nm; MOF crystal layer: A ZIF - 8 crystal layer grown in situ with amino groups as nucleation sites, with a thickness of 50 - 150 nm, a crystal size of 20 - 50 nm, and a pore size of 3.3 - 3.5 Å; Functionalized surface layer: Thiol groups distributed on the outer surface of the MOF crystal, with a sulfur element content of 0.5 - 2 wt%, and satisfying the following structural relationship: Among them, is the thiol group density, is the amino group density.

2. The silica hollow sphere with a MOF composite layer according to claim 1, wherein The cavity volume ratio of the kernel layer , and the hydroxyl density is 4.8 - 5.2 per nm²; The silane molecules of the amino - silane layer are in an upright orientation, and the molecular tilt angle measured by ellipsometry ≤ 15°; The thiol groups are located at the edges of the MOF crystal.

3. The manufacturing method of a silica hollow sphere according to claim 1, wherein, Including the following steps: S100. Pretreat the silica hollow spheres to activate the surface hydroxyl groups; S200. Aminate and modify the activated silica hollow spheres with a γ - aminopropyltriethoxysilane solution to obtain amino - functionalized silica; S300. Using amino groups as nucleation sites, in - situ grow a ZIF - 8 crystal layer in a methanol solution of zinc salt and 2 - methylimidazole; S400. React the product obtained in step S300 with a thioacetamide solution for surface thiolation modification.

4. The manufacturing method according to claim 2, characterized in that, In step S200, the concentration of the γ - aminopropyltriethoxysilane solution is 3 - 8 wt%, the reaction pH value is 4 - 6, the reaction temperature is 60 - 80 °C, and the reaction time is 4 - 8 hours.

5. The manufacturing method according to claim 2, wherein In step S300, the zinc salt is zinc nitrate, the zinc ion concentration is 0.05 - 0.2 M, the 2 - methylimidazole concentration is 0.3 - 0.6 M, the reaction temperature is 30 - 40 °C, and the reaction time is 8 - 24 hours.

6. The manufacturing method according to claim 2, characterized in that In step S400, the concentration of the thioacetamide solution is 0.3 - 0.8 M, the reaction temperature is 50 - 70 °C, the reaction time is 2 - 6 hours, and the sulfur element content of the obtained product is 0.5 - 2 wt%.

7. A method for predicting the dielectric loss of the silica hollow spheres according to claim 1 or 2, characterized in that, Including the following steps: a. Calculate the interfacial binding energy density by molecular dynamics simulation : Among them, is the repulsive term coefficient of the Lennard-Jones potential, is the attractive term coefficient of the Lennard-Jones potential, is the hydrogen bond interaction strength coefficient, is the decay coefficient of the hydrogen bond interaction, is the minimum interatomic interaction distance, is the stage radius; b. Establish a three - dimensional electric field distribution equation based on the finite element method: Among them, is the position-dependent relative permittivity, is the electric potential distribution function, is the interface polarization point and density, is the vacuum permittivity, effective charge quantity, is the number of interface dipoles per unit volume, is the reciprocal of the Boltzmann factor, is the interface binding strength parameter, is the absolute temperature; c. Construct a complex dielectric constant frequency - domain response function: wherein, is the high-frequency baseline dielectric constant, is the change in dielectric constant contributed by interfacial polarization, is the angular frequency, is the relaxation time, is the Cole-Cole distribution parameter, is the direct current conductivity; d. Obtain the total dielectric loss through vector superposition: Among them, is the volume fraction weight factor, is the interface bonding strength weight, is the activation energy correlation weight, is the dispersion correction term, is the norm of the dielectric constant gradient, is the distribution uniformity index.

8. The method for predicting the dielectric loss of the silica hollow spheres according to claim 7, characterized in that, In step a, the definition formula of the interface bonding strength parameter is: Among them, is the number of atom pairs counted, is the change in the atom pair spacing, is the partial derivative of the interfacial energy with respect to the atomic spacing.

9. The method for predicting the dielectric loss of the silica hollow spheres according to claim 7, characterized in that, In step c, by measuring the relaxation time at different temperatures , the activation energy is fitted , Activation energy The extraction method is as follows: Among them, is the pre-exponential factor, is the reference temperature, is the Boltzmann constant.

10. The method for predicting the dielectric loss of the silica hollow spheres according to claim 7, characterized in that, In step d, the calculation formula for the distribution uniformity index is as follows: Among them, is the position coordinate of the th packing particle, is the average value of the packing positions, is the standard deviation of the positions.

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