A method for calculating the scattering phase function of a plurality of arbitrarily shaped nanoparticles

Abstract

The application discloses a method for calculating scattering phase functions of multiple nanoparticles with arbitrary shapes, and mainly comprises the following steps: establishing a simulation model of nanoparticles; setting a calculation region of scattering energy; grid division; and simulation calculation. Based on the finite element simulation method, the application can break through the limitation of the number and shape of nanoparticles in the classical scattering phase function calculation method, realizes the solution of the scattering phase functions of multiple nanoparticles with arbitrary shapes, and provides a solution for studying the distribution of scattering energy of a nanoparticle system with arbitrary shapes in a three-dimensional space.

Description

Technical Field

[0001] This invention belongs to the field of nanomaterial simulation, and in particular, it is a method for calculating the scattering phase function of multiple nanoparticles of arbitrary shape. Background Technology

[0002] The scattering phase function, as one of the important optical properties of nanoparticles, is a parameter that expresses the spatial distribution characteristics of scattered light intensity, representing the distribution of incident energy with respect to the scattering angle after scattering by the particle. Studying the spatial distribution of scattered energy from nanoparticles is of great significance for understanding the radiative transfer characteristics of porous media, mastering the radiative transfer process of aerosol particles in the atmosphere, and achieving underwater wireless optical communication.

[0003] Currently, there are many methods for calculating the scattering phase function. For example, for spherical particles in a homogeneous medium, the scattering phase function can be obtained by rigorous Mie series solutions. The multi-sphere T-matrix method is a classic method for calculating the scattering phase function of multiple spherical nanoparticles. The Discrete Dipole Approximation (DDA) method is used to calculate the electromagnetic scattering characteristics of a single scatterer of arbitrary shape or a periodic structure. The Henyey-Greenstein (HG) phase function approximation method and its optimized counterparts, such as the Double Henyey-Greenstein (DHG) and Modified Double Henyey-Greenstein (MDHG) methods, can be used to calculate the scattering phase function of a single non-spherical particle and are currently widely used. However, all of these methods, whether obtaining exact analytical solutions or approximate solutions for the scattering phase function of nanoparticles, impose varying degrees of limitations on the shape, number, and even distribution of the nanoparticles.

[0004] However, in recent years, with the advancement of micro- and nano-fabrication technology and the development of science and technology, the shapes of nanoparticles have evolved from spherical to various shapes. Furthermore, there are increasingly more dense particle systems in nature and in the industrial field, such as clouds, raindrops, and aerosol particles in the atmosphere, the combustion of pulverized coal in furnaces, and the study of the characteristics of filler particles in functional nanomaterials. The spatial distribution of scattering energy of nanoparticle systems is one of the important factors affecting these thermal radiation transmission problems. Therefore, it is necessary to solve the scattering phase function problem of nanoparticle systems composed of multiple nanoparticles of arbitrary shapes. Summary of the Invention

[0005] To address the technical problem of the spatial distribution of scattering energy from multiple nanoparticles of arbitrary shapes, this invention provides a method for calculating the scattering phase function of multiple nanoparticles of arbitrary shapes.

[0006] The technical solution to achieve the purpose of this invention is as follows:

[0007] A method for calculating the scattering phase function of multiple nanoparticles of arbitrary shape includes the following steps:

[0008] Step 1, establish a nanoparticle simulation model:

[0009] From the outside in, the layers are: a perfect matching layer, a scattering energy receiving surface, an external environment dielectric layer, and nanoparticles. The scattering energy receiving sphere is located at the junction of the perfect matching layer and the external environment dielectric layer.

[0010] The energy-receiving sphere is divided into 181 sub-regions according to the directions corresponding to 181 scattering angles θ (0°~180°). The division method is as follows: First, add 180 working planes, select the plane type as xy plane, and set the z coordinates to h*sin(π / 180*89.5), h*sin(π / 180*88.5)……h*sin(π / 180*0.5), -h*sin(π / 180*0.5)……-h*sin(π / 180*88.5), -h*sin(π / 180*89.5) in sequence, where h is the radius of the energy-receiving sphere. Then, divide the 180 working planes with the energy-receiving sphere, and finally obtain 181 sub-regions on the energy-receiving sphere.

[0011] Step 2, set the calculation area for scattered energy:

[0012] Each region and the entire region on the sphere that receives scattered energy are set as the corresponding integration region;

[0013] The formula for calculating the scattering intensity in each sub-region is set as follows:

[0014]

[0015] Where i represents the scattering angle θ corresponding to the region, nrelPoav is the time average of the radiative power density, and S i This refers to the area of ​​the region;

[0016] The formula for calculating the average scattering intensity on the entire scattering energy receiving sphere is as follows:

[0017]

[0018] Where S is the area of ​​the entire sphere that receives scattered energy;

[0019] Step 3, Mesh Generation:

[0020] Mesh division was performed on the perfect matching layer, the external environment dielectric layer, and the nanoparticles;

[0021] Step 4, Simulation Calculation:

[0022] Set the formula for calculating the scattering phase function;

[0023] The formula for calculating the scattering phase function of nanoparticles at each scattering angle is set as follows:

[0024]

[0025] Where I i To receive the scattered energy, I represents the scattered intensity on each sub-region of the receiving sphere. a The average scattering intensity on the entire scattering energy receiving sphere;

[0026] Set electromagnetic field parameters, including the electromagnetic wave calculation region and background electric field parameters.

[0027] Compared with the prior art, the present invention has the following significant advantages:

[0028] (1) Using the finite element method to deal with the scattering problem of nanoparticles can overcome the limitations of classical methods for solving the scattering phase function, including the multi-sphere T matrix method, DDA method and Mie theory, on the shape, number and distribution of nanoparticles. By setting a scattering energy receiving sphere in the far field region far away from the nanoparticles, the scattering phase function of multiple nanoparticles with arbitrary distribution can be calculated, providing a powerful solution for obtaining the spatial distribution of scattering energy of nanoparticles with arbitrary shapes. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of a nanoparticle simulation model.

[0030] Figure 2 This is a schematic diagram of a rod-shaped nanoparticle system.

[0031] Figure 3 A comparison of the scattering phase function results for a single Te nanoparticle sphere.

[0032] Figure 4 A comparison of the scattering phase function results for two Te nanoparticle spheres.

[0033] Figure 5 A comparison of the scattering phase function results for three Te nanoparticle spheres.

[0034] Figure 6 The figure shows the scattering phase function of three Te nanoparticle rods as a function of aspect ratio AR.

[0035] Figure 7 The figure shows the scattering phase function of three Te nanoparticle rods as a function of the rod spacing l. Detailed Implementation

[0036] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. These descriptions are merely illustrative of how the present invention is implemented and should not be construed as limiting the present invention in any way.

[0037] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0038] Example 1

[0039] The present invention provides a method for calculating the scattering phase function of multiple nanoparticles of arbitrary shape, the specific steps of which are as follows:

[0040] Step 1, establish a nanoparticle simulation model:

[0041] Nanoparticle models, such as Figure 1 As shown, from the outside in, the layers are a perfect matching layer, a scattering energy receiving surface, an external environment dielectric layer, and nanoparticles, with the scattering energy receiving sphere located at the junction of the perfect matching layer and the external environment dielectric layer.

[0042] The energy-receiving sphere is divided into 181 sub-regions according to the directions corresponding to 181 scattering angles θ (0°~180°). The division method is as follows: First, add 180 working planes, select the plane type as xy plane, and set the z coordinates to h*sin(π / 180*89.5), h*sin(π / 180*88.5)……h*sin(π / 180*0.5), -h*sin(π / 180*0.5)……-h*sin(π / 180*88.5), -h*sin(π / 180*89.5) in sequence, where h is the radius of the energy-receiving sphere. Then, divide the 180 working planes with the energy-receiving sphere, and finally obtain 181 sub-regions on the energy-receiving sphere.

[0043] Step 2, set the calculation area for scattered energy:

[0044] Each region and the entire region on the sphere that receives scattered energy are set as the corresponding integration region;

[0045] The formula for calculating the scattering intensity in each sub-region is set as follows:

[0046]

[0047] Where i represents the scattering angle θ corresponding to the region, nrelPoav is the time average of the radiative power density, and S i This refers to the area of ​​the region;

[0048] The formula for calculating the average scattering intensity on the entire scattering energy receiving sphere is as follows:

[0049]

[0050] Where S is the area of ​​the entire sphere that receives scattered energy;

[0051] Step 3, Mesh Generation:

[0052] The perfect matching layer, the external environment dielectric layer, and the nanoparticles were meshed using a free tetrahedral mesh. The mesh size for the perfect matching layer and the external environment dielectric layer was set to λ / 6, where λ is the incident wavelength in nm; the mesh size for the nanoparticles was set to 10 nm.

[0053] Step 4, Simulation Calculation:

[0054] Set the formula for calculating the scattering phase function;

[0055] The formula for calculating the scattering phase function of nanoparticles at each scattering angle is set as follows:

[0056]

[0057] Where I i To receive the scattered energy, I represents the scattered intensity on each sub-region of the receiving sphere. a The average scattering intensity on the entire scattering energy receiving sphere.

[0058] Set electromagnetic field parameters, including the electromagnetic wave calculation region and background electric field parameters;

[0059] The formula for calculating the background electric field parameters is:

[0060] I0*exp(-j*(2π / λ*n*cos(alpha)*x+ewfd.k0*n*cos(beta)*y+ewfd.k0*n*cos(gamma)*z))

[0061] Where I0 is the incident electric field strength, and in this example, I0 = 1 V / m; j is the imaginary unit; n is the refractive index of the dielectric layer of the external environment, and in this example, it is the refractive index of water; alpha, beta, and gamma are the angles between the incident direction of the electromagnetic wave and the positive x-axis, positive y-axis, and positive z-axis, respectively. In this example, the incident direction of the electromagnetic wave is along the negative z-axis, so alpha is 90°, beta is 90°, and gamma is 180°; x, y, and z are unit vectors.

[0062] Results analysis:

[0063] The scattering phase function calculation results of nanoparticles with different shapes were compiled, and the calculation results of the scattering phase function of spherical nanoparticles were compared and verified with the classical phase function calculation method. The influence of the size parameter variation of non-spherical (such as rod-shaped) nanoparticles on the spatial distribution of their scattering energy was analyzed.

[0064] Figure 3 , Figure 4 , Figure 5 This is a comparison between the scattering phase function results calculated by this invention and the classical multi-sphere T-matrix method, wherein... Figure 2 The image shows a comparison of the scattering phase function results for a single Te nanoparticle sphere. Figure 3 The image shows a comparison of the scattering phase functions of two Te nanoparticle spheres discretely distributed within a 200 nm cubic space. Figure 4 The image shows a comparison of the scattering phase functions of three Te nanoparticle spheres discretely distributed within a 300 nm cubic space. The nanoparticle spheres have a diameter of 100 nm. Figures 3-5 The results show that when the incident wavelength is 300 nm, the scattering phase function of different numbers of spherical Te nanoparticles is mainly forward scattering; and the scattering phase function calculation results of the present invention are almost in agreement with the results of the classical multi-sphere T matrix method, proving the accuracy of the present invention.

[0065] Figure 6 The figure shows a rod-shaped nanoparticle system (physical model as shown). Figure 2 The figure shows the scattering phase function as a function of aspect ratio AR, where AR is the ratio of the length to the diameter of the rod-shaped nanoparticles. The diameter of the nanoparticles is 60 nm, the spacing between the rods is 60 nm, the incident light wavelength is 900 nm, propagating in the negative z-axis direction, and the electric field is polarized in the x-axis direction. Figure 3 The results show that by increasing the length of the nanorods, the size parameter of the rod-shaped nanoparticle system in the direction parallel to the incident light increases. At this time, the scattering phase function becomes larger and larger in the entire forward direction (scattering angle θ < 90°), while it becomes smaller and smaller in the entire backward direction (90° < θ < 180°). This indicates that increasing the size parameter of the rod-shaped nanoparticle system in the direction parallel to the incident light can increase the proportion of scattering energy in the forward direction and decrease the proportion of scattering energy in the backward direction.

[0066] Figure 7 The figure shows a rod-shaped nanoparticle system (physical model as shown). Figure 2 The scattering phase function (shown) varies with the rod spacing *l*, where *l* is 0, *d*, and 2 *d*, where *d* is the diameter of the nanorod (60 nm), the rod length is 120 nm, the incident light wavelength is 900 nm, propagating in the negative z-axis direction, and the electric field is polarized in the x-axis direction. Figure 4The results show that by increasing the spacing l between the nanorods, the size parameter of the rod-shaped nanoparticle system in the direction perpendicular to the incident light increases. At this time, the scattering phase function becomes larger in the forward (0° < θ < 60°) and backward (120° < θ < 180°) spatial regions, while it becomes smaller in the lateral (60° < θ < 120°) region. This indicates that increasing the size parameter of the rod-shaped nanoparticle system in the direction perpendicular to the incident light can increase the proportion of forward and backward scattering energy, while reducing the proportion of lateral scattering energy.

Claims

1. A method of calculating the scattering phase function of a plurality of arbitrarily shaped nanoparticles, characterized by, Includes the following steps: Step 1, establish a nanoparticle simulation model: From the outside in, the layers are: a perfect matching layer, a scattering energy receiving surface, an external environment dielectric layer, and nanoparticles. The scattering energy receiving sphere is located at the junction of the perfect matching layer and the external environment dielectric layer. The scattering energy receiving spherical surface is divided into 181 sub-regions according to 181 scattering angles In The range is divided into 181 sub-regions, and the division method is: first, add 180 working planes, the plane type is selected as the xy plane, and the z coordinate is set as , ... , ... , , wherein is the radius of the scattering energy receiving spherical surface, then the 180 working planes are respectively divided with the scattering energy receiving spherical surface, and finally 181 sub-regions are obtained on the scattering energy receiving spherical surface; Step 2, set the calculation area for scattered energy: Set each region and the entire region on the sphere that receives the scattered energy as the corresponding integration region, and set the formula for calculating the scattering intensity; The formula for calculating the scattering intensity on each sub-region of the scattering energy receiving sphere is as follows: ； where i represents the scattering angle corresponding to the region , is the time average of the radiation power density, is the area of the region; The average scattering intensity calculation formula on the whole scattering energy receiving spherical surface is set as: ; wherein A is the area of the entire receiving sphere of scattered energy; Step 3, Mesh Generation: Mesh division was performed on the perfect matching layer, the external environment dielectric layer, and the nanoparticles; Step 4, Simulation Calculation: Set the formula for calculating the scattering phase function; set the electromagnetic field parameters, including the electromagnetic wave calculation region and the background electric field parameters; The formula for calculating the scattering phase function of nanoparticles at each scattering angle is set as follows: ； wherein is the scattering intensity on each sub-area on the scattering energy receiving sphere, is the average scattering intensity on the whole scattering energy receiving sphere.

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