Preparation method of nanostructure-oriented self-cleaning radiant cooling material

Abstract

The application discloses a preparation method of a nano-structure-oriented self-cleaning radiation refrigeration material, and the method comprises the following steps: step 1, designing an initial nano-structure model of the self-cleaning radiation refrigeration material as a multi-scale periodic nanocrystal with embedded functional groups of different scales; step 2, based on the initial nano-structure model, performing multi-scale simulation by using molecular dynamics to minimize the total energy of the model and obtain a stable structure, and obtaining the nano-structure model at this time; and step 3, preparing the self-cleaning radiation refrigeration material based on the nano-structure model. The method can realize efficient radiation and persistent self-cleaning performance in a wide frequency spectrum range, ensure the thermodynamic stability and long-term performance of the material, reduce maintenance costs, and improve the application value of the material.

Description

Technical Field

[0001] This invention relates to the field of materials preparation, and in particular to a method for preparing nanostructure-guided self-cleaning radiative cooling materials. Background Technology

[0002] Nanostructure-guided self-cleaning radiative cooling materials, as an emerging functional material, have attracted widespread attention in recent years in the fields of energy, environment, and construction. With the intensification of global climate change and the energy crisis, how to effectively utilize natural resources for cooling and reduce energy consumption has become a research hotspot. Radiative cooling is a technology that utilizes the efficient radiative properties of materials within a specific wavelength range to achieve cooling by radiating heat into outer space. Compared to traditional mechanical cooling methods, radiative cooling has the advantages of being energy-free, pollution-free, and highly efficient. However, existing radiative cooling materials still face many problems in practical applications, such as surface contamination and performance degradation, which limit their large-scale application and promotion.

[0003] In current technologies, research on radiation cooling materials mainly focuses on the following aspects: Traditional radiation cooling materials often employ metal oxides (such as titanium dioxide and alumina) and polymer materials (such as polytetrafluoroethylene). These materials exhibit good reflection and emission properties in the ultraviolet and infrared bands. However, the performance optimization of single-scale structures of these materials within specific wavelength ranges is limited, making it difficult to achieve efficient radiation across a wide spectral range. To improve the self-cleaning properties of materials, researchers have attempted to introduce hydrophobic or hydrophilic groups onto the material surface, achieving surface functionalization through surface modification techniques (such as chemical vapor deposition and solution treatment). However, these methods are prone to failure during long-term use, and the stability and durability of surface functional groups are difficult to guarantee, leading to a gradual weakening of the material's self-cleaning effect. Molecular dynamics simulation, as an important research tool, is widely used in the design and optimization of nanomaterials. By simulating the dynamic behavior and energy changes of materials under different conditions, the structural design and performance optimization of materials can be guided. However, existing simulation techniques mainly focus on single-scale models, lacking systematic research on multi-scale structures and complex functional groups, resulting in a gap between simulation results and practical applications. Summary of the Invention

[0004] The purpose of this invention is to provide a method for preparing nanostructure-guided self-cleaning radiation cooling materials, which can achieve high-efficiency radiation and long-lasting self-cleaning performance over a wide frequency range, ensure the thermodynamic stability and long-term performance of the materials, reduce maintenance costs, and improve the application value of the materials.

[0005] To address the aforementioned technical problems, this invention provides a method for preparing a nanostructure-guided self-cleaning radiation cooling material, the method comprising:

[0006] Step 1: The initial nanostructure model of the self-cleaning radiation cooling material is designed as a multi-scale periodic nanocrystal with embedded functional groups of different scales;

[0007] Step 2: Based on the initial nanostructure model, perform multi-scale simulations using molecular dynamics to minimize the total energy of the model and obtain a stable structure, thus obtaining the nanostructure model at this point.

[0008] Step 3: Based on the nanostructure model, prepare self-cleaning radiation cooling materials.

[0009] Furthermore, step 1 specifically includes: defining the size and volume of the basic unit cell; embedding multiple functional groups at various scales into the basic unit cell, with each functional group having its volume calculated based on its geometry; replicating the basic unit cell in three-dimensional space to form a periodic structure; and calculating the total volume of the initial nanostructure model to ensure consistency of the structure at each scale and the periodic boundary conditions.

[0010] Furthermore, the total volume of the initial nanostructure model is expressed using the following formula:

[0011]

[0012] Among them, V initial N represents the total volume of the initial nanostructure model. x N y and N z These represent the number of times the basic unit cell is replicated along the X, Y, and Z axes in three-dimensional space, respectively; s represents the number of scales for embedding functions; m i V represents the number of functional groups at the i-th scale; ij Let i be the volume of the j-th functional group at the i-th scale; at each scale, the embedded functional groups are described and simulated by three types of particles, including: classical particles, quantum particles and macroscopic particles; i and j are both subscript indices.

[0013] Furthermore, step 2 specifically includes: for each embedded functional group at each scale, initializing the position of its i-th classical particle as r. i (0), velocity is v i (0); initialize the wave function of its i-th quantum particle as ψ i (r, 0); initialize the position of its i-th macroscopic particle as R. i (0), velocity is V i (0); At each time step, update the displacement and velocity of the classical particle using the classical particle motion equations, update the position and velocity of the quantum particle by solving the time-dependent Schrödinger equation, and update the displacement and velocity of the macroscopic particle using the macroscopic particle motion equations; calculate the interaction potential energy; within each time step Δt, iterate through the following steps until the total energy E of the model is reached.total Both the quantum state density matrix ρ(r) and the quantum state density matrix satisfy the convergence condition: calculate the current total energy. Update the state of all particles and recalculate the force and potential energy; where r = (x, y, z) is the position vector of the particle in space, and x, y and z are the components of the position vector on the three coordinate axes, respectively.

[0014] Furthermore, the current total energy is calculated using the following formula.

[0015]

[0016] in, This represents the summation over all classical particles; N is the total number of classical particles; p i Let m be the momentum of the i-th classical particle; i Let V(r) be the mass of the i-th classical particle; i Let ) be the position of the i-th classical particle at position r. i Potential energy at the point; U ij (r i r j Let be the interaction potential energy between the i-th and j-th classical particles; For the summation over all quantum particles; ∈ j Let α be the energy eigenvalue of the j-th quantum particle; j The energy coupling coefficient associated with quantum particles; |ψ j (r j )| 2 For the wave function of the j-th quantum particle at position r j The probability density at that location; To sum over all macroscopic particles; P k M represents the momentum of the k-th macroscopic particle; k V is the mass of the kth macroscopic particle; int (R k ) represents the position R of the k-th macroscopic particle. k Internal interaction potential energy at the location; W kl (R k R l Γ represents the interaction potential energy between the k-th and l-th macroscopic particles; ij (r i , ψ j ) represents the interaction energy between the i-th classical particle and the j-th quantum particle; Ξ km (R k r m ) represents the interaction energy between the k-th macroscopic particle and the m-th classical particle; M represents the number of quantum particles; L represents the number of macroscopic particles; k represents the subscript index; l represents the subscript index.

[0017] Furthermore, the total energy E of the model total The convergence condition is expressed by the following formula:

[0018]

[0019] in, This represents the total energy in the nth iteration. The total energy in the (n+1)th iteration; ΔE is the energy change; ∈ E The energy convergence threshold is a preset positive number; the convergence condition of the quantum state density matrix ρ(r) is expressed by the following formula:

[0020] Δρ=∫|ρ (n+1) (r)-ρ (n) (r)|dr<∈ ρ ;

[0021] Where, ρ (n) (r) is the quantum state density matrix of the nth iteration; ρ (n+1) (r) is the quantum state density matrix of the (n+1)th iteration; Δρ is the change in the density matrix; ∈ ρ The convergence threshold of the density matrix is ​​a preset positive number.

[0022] Furthermore, at each time step, the formulas for updating the displacement and velocity of the classical particle using the classical particle motion equations are as follows:

[0023]

[0024] Where, r i (t) is the position vector of the i-th classical particle at time t; r i (t+Δt) is the position vector of the i-th classical particle at time t+Δt; v i (t) is the velocity vector of the i-th classical particle at time t; v i (t+Δt) is the velocity vector of the i-th classical particle at time t+Δt; Δt is the time step; a i (t) represents the acceleration of the i-th classical particle at time t; b i (t) is the time derivative of the acceleration of the i-th classical particle at time t; γ is the external force acting on the i-th classical particle at time t; i is the external field coupling coefficient, used to describe the interaction strength between the i-th classical particle and the external force field.

[0025] Furthermore, when updating the position and velocity of a quantum particle by solving the time-dependent Schrödinger equation, the time-dependent Schrödinger equation is expressed using the following formula:

[0026]

[0027] Where, ψ j (r, t) is the wave function of the j-th quantum particle at time t; It is Planck's constant; Let m be the Laplace operator of the j-th quantum particle; j V is the mass of the j-th quantum particle; eff (r j ,t) represents the position of the j-th quantum particle at position r j and the effective potential at time t; g|ψ j (r, t)| 2 The term ∑ represents a nonlinear term describing the self-interaction of quantum particles. k λ k cos(ω k t)r j ·E k (t) represents the time-dependent external field term, where λ k ω is the coupling coefficient. k For frequency, E k (t) represents the external electric field at time t;

[0028] ψ j (r, t+Δt)=U(t+Δt, t)ψ j (r, t);

[0029] Where U(t+Δt, t) is the time evolution operator, expressed by the following formula:

[0030]

[0031] Where V is the kinetic energy part of the Hamiltonian operator; T is the potential energy part of the Hamiltonian operator; and δ is the imaginary number symbol.

[0032] Furthermore, the displacement and velocity of the macroscopic particles are updated using the following formula based on the equations of motion of the macroscopic particles:

[0033]

[0034] Among them, R k (t) represents the position of the k-th macroscopic particle at time t; R k (t+Δt) represents the position of the k-th macroscopic particle at time t+Δt; V k (t) represents the velocity of the k-th macroscopic particle at time t; V k(t+Δt) is the velocity of the k-th macroscopic particle at time t+Δt; A k (t) represents the acceleration of the k-th macroscopic particle at time t; A k (t+Δt) represents the acceleration of the kth macroscopic particle at time t+Δt.

[0035] The nanostructure-guided self-cleaning radiative cooling material preparation method of this invention has the following beneficial effects: Firstly, this invention significantly improves the radiative cooling efficiency of the material through the design of a multi-scale periodic nanocrystal structure. Traditional radiative cooling materials mostly employ single-scale nanostructures. This design can achieve good radiation performance within a specific wavelength range, but its effectiveness is limited over a wide spectrum. This invention introduces a multi-scale structure, where nanocrystal units of different sizes optimize the material's reflection and emission properties in the ultraviolet, visible, and infrared bands, thereby achieving efficient radiation over a wider spectrum. This multi-scale design allows the material to more effectively reflect sunlight and radiate heat, thus significantly reducing surface temperature and improving radiative cooling efficiency. Secondly, this invention utilizes molecular dynamics simulation technology to optimize the nanostructure at multiple scales, ensuring the material's thermodynamic stability and functional performance. Molecular dynamics simulation can accurately capture the dynamic behavior and energy changes of the nanostructure under different temperature and pressure conditions. By minimizing the total energy, a structure with the lowest system energy and stability is found. This optimization process not only improves the material's stability but also ensures its long-term performance and durability in practical applications. Through multi-scale simulations, this invention can systematically study the interactions between structures and functional groups at different scales in materials, providing more accurate theoretical guidance and thus achieving optimal structural design. Furthermore, this invention achieves self-cleaning functionality by embedding chemical groups with specific functions into the nanocrystalline structure. Traditional surface modification methods are prone to failure during long-term use, while this invention, by introducing functional groups, such as hydrophilic and hydrophobic groups, into the multi-scale structure and fixing them in the nanocrystals through chemical bonds or physical adsorption, ensures the stability and durability of the functional groups. For example, hydrophilic groups can form a water film on the material surface, making it easy for dirt to be washed away; hydrophobic groups can reduce the surface energy, causing water droplets to form spheres on the surface and roll off, carrying away surface dirt. Through this embedded design, the material can maintain a clean surface during use, reducing maintenance costs. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0037] Figure 1 This is a schematic flowchart of a method for preparing a nanostructure-guided self-cleaning radiation cooling material according to an embodiment of the present invention. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] Example 1: Reference Figure 1 A method for preparing a nanostructure-guided self-cleaning radiation cooling material, the method comprising:

[0040] Step 1: The initial nanostructure model of the self-cleaning radiation cooling material is designed as a multi-scale periodic nanocrystal with embedded functional groups of different scales;

[0041] Multiscale periodic nanocrystals are materials with specific structures at both the micro and nanoscale. These structures allow for the comprehensive optimization of optical, thermal, and mechanical properties by controlling material characteristics at different scales. Nanocrystals are typically formed from atoms, molecules, or ions through self-assembly or precision synthesis methods. Their periodic arrangement can be repeated at specific spatial scales, resulting in synergistic effects on different physical properties. For example, in radiative cooling processes, materials require high solar reflectivity and high thermal infrared emissivity; multiscale structures can optimize these properties separately in the ultraviolet, visible, and infrared bands. Embedded functional groups refer to the introduction of specific functional groups into nanocrystals to achieve specific functions, such as self-cleaning. Self-cleaning is usually achieved by introducing hydrophilic or hydrophobic chemical groups. Hydrophilic groups, such as hydroxyl (-OH) and carboxyl (-COOH), can form a water film on the material surface, making it easy for dirt to be washed away. Hydrophobic groups, such as fluoroalkyl (-CF3), can lower the energy of the material surface, causing water droplets to form spherical shapes and roll off, thus carrying away surface dirt. Furthermore, by introducing photocatalytic functional groups, such as titanium dioxide (TiO2), reactive oxygen species can be generated under ultraviolet light irradiation to decompose organic pollutants on the surface, achieving a self-cleaning effect. The process of designing the initial nanostructure model involves multiple steps and principles. First, suitable nanocrystalline materials need to be selected, typically including metal oxides, carbon-based materials, and polymers. These materials possess excellent physical and chemical properties at the nanoscale, such as high surface area, excellent mechanical strength, and chemical stability. Then, through computational simulation and experimental optimization, the crystal structure and arrangement of the material are determined. The key to multi-scale design lies in achieving the control of the macroscopic properties of the material through the combination of nanostructure units of different sizes. For example, large-sized nanocrystals can improve the mechanical strength and stability of the material, while small-sized nanocrystals can be used to optimize the optical and thermal properties. Molecular dynamics simulation is an important tool in the design process. Molecular dynamics simulation can simulate the behavior of nanostructures under different temperature and pressure conditions, predicting the stability and performance of the material. By calculating the total energy of the material, the optimal nanostructure design can be found. Total energy typically includes bond energy, angular energy, dihedral angle energy, and non-bonded energy. These energy terms describe the interactions between atoms in the nanostructure. Bond energy describes the strength of the chemical bonds between atoms, angular energy describes the angular change energy between chemical bonds, dihedral angle energy describes the torsional energy between different planes within the molecule, and non-bonded energies include van der Waals forces and electrostatic interactions. By optimizing these energy terms, a thermodynamically stable nanostructure model can be obtained.

[0042] Step 2: Based on the initial nanostructure model, perform multi-scale simulations using molecular dynamics to minimize the total energy of the model and obtain a stable structure, thus obtaining the nanostructure model at this point.

[0043] Molecular dynamics simulation is a computer simulation method that studies the trajectory of each atom in a system by numerically solving classical mechanical equations. The core of this simulation method lies in the potential function, which describes the interaction forces between atoms. The potential function typically includes multiple components such as bond energy, angular energy, dihedral angle energy, and non-bonded energy. These energy terms describe different types of interactions between atoms in a nanostructure. By optimizing these energy terms, a structure with the lowest energy and greatest stability can be obtained, thus ensuring the thermodynamic stability of the material. Thermodynamically, a system tends towards the lowest energy state, which is a natural tendency for the system to reach equilibrium and stability. Minimizing the total energy means that the interactions between atoms and molecules within the system have reached an optimal equilibrium state, capable of resisting changes in the external environment and internal disturbances. For nanostructured materials, the structure with the lowest energy usually means the most compact atomic arrangement and the most reasonable bond angles and bond lengths, thus enabling the material to exhibit optimal mechanical, thermal, and optical properties. In molecular dynamics simulations, the simulation process is initiated by setting initial conditions, including the initial positions, velocities, and boundary conditions of the atoms. The initial nanostructure model provides a rough atomic arrangement, but this arrangement may not be optimal. Molecular dynamics simulations can simulate the dynamic behavior of nanostructures under different temperature and pressure conditions, observing how atoms and molecules move and rearrange to reach a state of minimum energy. During the simulation, the total energy of the system typically includes the following components: bond energy (describing the strength of chemical bonds between atoms), angular energy (describing the angular change energy between chemical bonds), dihedral energy (describing the torsional energy between different planes within the molecule), and non-bonded energy (including van der Waals forces and electrostatic interactions). These energy terms collectively determine the stability and structural properties of the system. By optimizing these energy terms, a structure with minimum energy and high stability can be found. Specifically, bond energy describes the strength of the chemical bond between two atoms. When the distance between atoms is at a certain equilibrium position, the bond energy reaches its minimum, indicating that the system is most stable at this position. Angular energy describes the angular change energy between three atoms; when the bond angle formed by the three atoms is close to the ideal angle, the angular energy is minimum, and the system is most stable. Dihedral energy describes the dihedral change energy between four atoms; a reasonable dihedral arrangement can reduce the system's energy and increase its stability. Nonbonded energies include van der Waals forces and electrostatic interaction energies. These energy terms describe short-range attractive and repulsive forces between atoms, as well as long-range electrostatic forces. These interactions have a significant impact on the overall stability of the system. During the simulation, the system gradually approaches a minimum energy state through repeated iterations and energy minimization. This process can be achieved using numerical optimization algorithms, such as the conjugate gradient method, Newton's method, or common algorithms in molecular dynamics simulations (such as the Verlet algorithm or the Leapfrog algorithm).These algorithms continuously adjust the positional information of atoms, gradually decreasing the total energy of the system until a minimum energy state is reached. In this state, the atoms and molecules are most tightly packed, internal stress is minimal, energy is lowest, and the system is most stable. In this way, a stable nanostructure model can be obtained. This model not only exhibits thermodynamic stability in the simulation environment but also remains stable during actual fabrication and application. Experimentally, methods to verify this stability typically include testing the material's mechanical strength, thermal stability, and environmental tolerance. These test results demonstrate the superior performance of the nanostructure optimized through molecular dynamics simulations in practical applications.

[0044] Step 3: Based on the nanostructure model, prepare self-cleaning radiation cooling materials.

[0045] Based on the optimized nanostructure model, suitable materials and synthesis methods need to be selected. There are various methods for synthesizing nanomaterials, such as chemical vapor deposition (CVD), solution processing, and sputtering. CVD can form high-purity, high-quality nanofilms on substrate surfaces; by controlling the type and flow rate of reactant gases, as well as deposition temperature and time, the formation of nanostructures can be precisely controlled. Solution processing is suitable for large-scale preparation, forming the desired nanostructures through the self-assembly of nanoparticles in solution. Sputtering can deposit nanomaterials at lower temperatures and is suitable for temperature-sensitive substrates. During material synthesis, special attention needs to be paid to the uniformity and consistency of the nanostructures. Since the size and arrangement of nanostructures have a significant impact on the material's radiative cooling and self-cleaning properties, process parameters must be strictly controlled during synthesis to ensure that the final material has a uniform nanostructure. For example, in CVD, by precisely controlling the flow rate of reactant gases and deposition time, nanofilms with uniform thickness and pore size distribution can be formed. In solution processing, by adjusting the solution concentration and reaction temperature, the growth rate and size distribution of nanoparticles can be controlled, thereby achieving uniform nanostructures. After material synthesis, assembly and post-processing steps are required. The purpose of this process is to assemble the synthesized nanomaterials into structures with practical application value and to functionalize their surfaces. Common assembly methods include spin coating, spray coating, and layer-by-layer self-assembly. These methods can uniformly coat nanomaterials onto a substrate surface, forming a thin film with the desired structure and properties. For example, spin coating can form a uniform nanofilm on a substrate, while spray coating is suitable for large-area coating and can rapidly form the desired nanostructure. Post-processing steps mainly include surface functionalization and stabilization treatment. Surface functionalization refers to introducing specific functional groups onto the surface of nanomaterials to achieve self-cleaning functionality. Common methods include chemical modification and physical adsorption. Chemical modification involves introducing hydrophilic or hydrophobic chemical groups, such as hydroxyl, carboxyl, or fluoroalkyl groups, through chemical reactions on the surface of nanomaterials. Physical adsorption uses electrostatic interactions or van der Waals forces to adsorb functional groups onto the surface of nanomaterials. For example, introducing hydrophobic groups onto the surface of a nanostructure can cause water droplets to form spheres and roll off, carrying away surface dirt and thus achieving self-cleaning functionality. Stabilization treatment refers to enhancing the stability of nanomaterials through physical or chemical methods to prevent degradation or performance decline during practical use. For example, heat treatment can improve the crystallinity and mechanical strength of nanomaterials, while surface modification can enhance their oxidation resistance and weather resistance. During the preparation process, a series of performance tests are required to ensure that the material possesses the expected self-cleaning and radiative cooling properties. Commonly used testing methods include spectral analysis, contact angle testing, and mechanical strength testing. Spectroscopic analysis is used to measure the reflectivity and emissivity of the material to determine its radiative cooling performance.Contact angle testing is used to assess the hydrophilicity or hydrophobicity of a material surface, thereby determining its self-cleaning performance. Mechanical strength testing is used to evaluate the mechanical properties of a material, ensuring its durability and stability in practical applications.

[0046] Specifically, titanium dioxide (TiO2) is used as the main component due to its excellent photocatalytic performance and high reflectivity. Titanium dioxide can generate highly oxidizing free radicals under ultraviolet light irradiation, decomposing organic pollutants and thus achieving a self-cleaning effect. To further enhance the material's radiative cooling performance, metal oxides, such as aluminum oxide (Al2O3) and zinc oxide (ZnO), are introduced into the titanium dioxide matrix. These materials exhibit good radiation performance in the infrared band. Next, a multi-scale periodic nanocrystal structure is designed. The initial design involves arranging titanium dioxide, aluminum oxide, and zinc oxide nanoparticles of different sizes in a specific ratio and periodicity to form a multi-scale structure. This multi-scale structure can be prepared using the sol-gel method. First, a sol solution containing different metal oxides is prepared, and then nanoparticles are formed through a sol-gel conversion process. These nanoparticles will undergo further processing to form a periodically arranged multi-scale nanocrystal structure. By adjusting the concentration and ratio of nanoparticles in the solution, the final nanostructure of the material can be precisely controlled. In the multi-scale structure, the smaller nanoparticles are mainly used to enhance the material's photocatalytic and reflective properties. Titanium dioxide particles with diameters between 10 and 50 nanometers were selected. These particles exhibit excellent photocatalytic activity under ultraviolet light, enabling them to decompose organic pollutants. Simultaneously, these small particles also improve the material's ultraviolet reflectivity, reducing solar energy absorption. Medium-sized nanoparticles, such as alumina particles ranging from 50 to 200 nanometers, are primarily used to enhance the material's mechanical strength and stability. Large nanoparticles, such as zinc oxide particles ranging from 200 to 500 nanometers, significantly improve the material's radiation performance in the infrared band, promoting heat dissipation. The design of embedded functional groups is also a crucial step. To achieve self-cleaning functionality, a combination of hydrophilic and hydrophobic groups was introduced into the nanocrystalline structure. Hydrophilic groups, such as hydroxyl (-OH) and carboxyl (-COOH) groups, can be introduced onto the surface of titanium dioxide and alumina particles through chemical modification. These hydrophilic groups can form a water film on the material surface. When water comes into contact with the surface, the water film covers the entire surface and flows under gravity, carrying away surface contaminants. Hydrophobic groups, such as fluoroalkyl groups (-CF3), are immobilized on the surface of zinc oxide particles through physical adsorption. These groups significantly reduce the surface energy of the material, causing water droplets to form spherical shapes and carry away dirt as they roll across the surface. Chemical vapor deposition (CVD) is used to introduce these embedded functional groups. In CVD, reactive gases are introduced into the nanocrystalline structure, decompose at high temperatures, and deposit on the surface of the nanoparticles to form the desired functional groups. By precisely controlling reaction conditions, such as temperature, gas flow rate, and reaction time, different functional groups can be introduced into different parts of the nanostructure, enabling multifunctional material design. Molecular dynamics simulation is an important tool in the design process.Molecular dynamics simulations can predict the behavior and properties of different nanostructures under various conditions. Simulation results show that multi-scale structures significantly improve the thermodynamic stability and radiation properties of materials, while embedded functional groups effectively achieve self-cleaning functions. These simulation results provide important theoretical basis for optimizing material design. In the actual preparation process, a sol solution containing titanium dioxide, aluminum oxide, and zinc oxide was first prepared, and nanoparticles were formed using the sol-gel method. These nanoparticles were then uniformly coated onto a substrate using spin-coating or spraying methods to form a thin film with a multi-scale structure. Next, hydrophilic and hydrophobic functional groups were introduced onto the film surface using CVD technology, ultimately forming a nanostructured material with self-cleaning and radiation-cooling functions. To verify the performance of this material, several experimental tests were conducted. Spectroscopic results show that the material has high reflectivity in the ultraviolet band and high emissivity in the infrared band, meeting the requirements for radiation cooling. Self-cleaning tests show that the material can effectively decompose organic pollutants after exposure to ultraviolet light, while the surface remains clean after rinsing with water. Furthermore, mechanical strength and stability tests also show that the multi-scale nanostructure significantly enhances the durability and service life of the material.

[0047] Example 2: Step 1 specifically includes: defining the size and volume of the basic unit cell; embedding multiple functional groups of various scales in the basic unit cell, with each functional group having its volume calculated based on its geometry; replicating the basic unit cell in three-dimensional space to form a periodic structure; and calculating the total volume of the initial nanostructure model to ensure consistency of the structure at each scale and the periodic boundary conditions.

[0048] Specifically, the basic unit cell is the smallest repeating unit of a material, containing the arrangement information of all the atoms or molecules that make up the material. Choosing an appropriate unit cell size and volume is crucial, as it directly affects the material's physical properties, such as optical, thermal, and mechanical properties. The definition of the basic unit cell is usually based on the material's crystal structure and desired function. For example, for self-cleaning radiative cooling materials, crystal structures with high symmetry and stability, such as face-centered cubic (FCC) or body-centered cubic (BCC) structures, might be chosen. Precise definition of the unit cell size and volume ensures the formation of stable periodic structures during replication and arrangement. Embedding functional groups at multiple scales within the basic unit cell is a key step. These functional groups endow the material with specific functions, such as self-cleaning and radiative cooling capabilities. The selection and arrangement of functional groups need to consider their geometry and volume to ensure precise embedding within the basic unit cell. For example, titanium dioxide nanoparticles with photocatalytic properties can be selected as functional groups and embedded at specific locations within the unit cell. The volume of each functional group is calculated based on its geometry to ensure a reasonable arrangement of these functional groups within the basic unit cell and to avoid spatial overlap or structural instability. The geometry of functional groups can be spherical, cylindrical, or other complex shapes. By calculating their volume, the filling rate of basic unit cells and the density of functional groups can be precisely controlled. Replicating basic unit cells in three-dimensional space to form periodic structures is a crucial step in constructing macroscopic materials. By replicating basic unit cells in three-dimensional space, nanostructures with periodic arrangements can be formed. This periodic structure can significantly affect the overall properties of the material, especially in optical and thermal properties. For example, through periodic arrangement, photonic band gaps can be formed within the material, effectively reflecting light of specific wavelengths and enhancing radiative cooling. During replication, it is necessary to ensure that the arrangement of each basic unit cell is consistent and that the boundary conditions between adjacent unit cells are matched to maintain the integrity and stability of the structure. Calculating the total volume of the initial nanostructure model is an important step in verifying the rationality of the design. By calculating the total volume, the consistency of the structure and periodic boundary conditions at each scale can be confirmed. The purpose of this step is to ensure that all functional groups and unit cells are reasonably distributed in the overall structure, without overfilling or voids. For example, by calculating the total volume of the initial nanostructure model, the density and porosity of the material can be determined; these parameters are crucial to the actual properties of the material. Ensuring overall volume consistency helps achieve uniform material properties and avoids performance degradation or failure due to structural inhomogeneity.

[0049] Example 3: The total volume of the initial nanostructure model is expressed using the following formula:

[0050]

[0051] Among them, V initial N represents the total volume of the initial nanostructure model. xN y and N z These represent the number of times the basic unit cell is replicated along the X, Y, and Z axes in three-dimensional space, respectively; s represents the number of scales for embedding functions; m i V represents the number of functional groups at the i-th scale; ij Let i be the volume of the j-th functional group at the i-th scale; at each scale, the embedded functional groups are described and simulated by three types of particles, including: classical particles, quantum particles and macroscopic particles; i and j are both subscript indices.

[0052] Specifically, the basic unit cell is the smallest repeating unit of a nanostructure, and its size and volume determine the fundamental physical properties of the material. Defining the lattice parameters and volume of the basic unit cell is a crucial step, as it directly affects the structural stability and functional realization of the material. The basic unit cell endows the material with specific functions by embedding functional groups at multiple scales. The volumes of these functional groups are precisely calculated based on their geometry and material density, ensuring their rational arrangement within the basic unit cell. Next, the basic unit cell is replicated in three-dimensional space to form a periodic structure. This periodic arrangement not only ensures that the macroscopic size and shape of the material adapt to different application requirements but also significantly improves the overall performance of the material. For example, by precisely controlling the number of repetitions of the basic unit cell in different directions, the size of the material can be adjusted to suit applications such as large-area coatings. During replication, it is necessary to ensure that the arrangement of each basic unit cell is consistent and that the boundary conditions between adjacent unit cells are matched to maintain the integrity and stability of the structure. Furthermore, the embedded functional groups function at different scales, endowing the material with multi-level functional properties. These functional groups may include photocatalytic nanoparticles to improve self-cleaning capabilities and thermal radiation functional groups to enhance radiative cooling performance. By precisely calculating and optimizing the geometry and volume of functional groups, we ensure their proper embedding and uniform distribution within the basic unit cell. To describe and simulate functional groups at different scales, three types of particle models are employed: classical particles, quantum particles, and macroscopic particles. Classical particles describe nanoscale atoms and molecules, simulating their behavior through classical mechanics; quantum particles describe functional groups significant at the quantum scale, simulating their behavior through quantum mechanics; and macroscopic particles describe functional groups at even larger scales, simulating their behavior through continuum mechanics. Through the comprehensive simulation of these three types of particles, we can fully describe the behavior of materials at different scales, ensuring the stability and functionality of the designed nanostructure models in practical applications.

[0053] Example 4: Step 2 specifically includes: For each embedded functional group at each scale, initialize the position of its i-th classical particle to r. i (0), velocity is v i (0); initialize the wave function of its i-th quantum particle as ψ i(r, 0); initialize the position of its i-th macroscopic particle as R. i (0), velocity is V i (0); At each time step, update the displacement and velocity of the classical particle using the classical particle motion equations, update the position and velocity of the quantum particle by solving the time-dependent Schrödinger equation, and update the displacement and velocity of the macroscopic particle using the macroscopic particle motion equations; calculate the interaction potential energy; within each time step Δt, iterate through the following steps until the total energy E of the model is reached. total Both the quantum state density matrix ρ(r) and the quantum state density matrix satisfy the convergence condition: calculate the current total energy. Update the state of all particles and recalculate the force and potential energy; where r = (x, y, z) is the position vector of the particle in space, and x, y and z are the components of the position vector on the three coordinate axes, respectively.

[0054] Specifically, for each functional group embedded at each scale, the states of various particles need to be initialized. The position r of the i-th classical particle... i (0) and velocity v i (0) represents its initial state. Classical particles are mainly used to describe atoms and molecules at the nanoscale, simulating their motion using classical mechanics. Initializing the state of these particles is essential for accurately calculating their trajectories and interactions in subsequent simulations. Precise initial conditions ensure that the starting state of the simulation matches the actual situation, thereby improving the accuracy and reliability of the simulation. The initialization of quantum particles is more complex. The wave function ψ of the i-th quantum particle... i (r, 0) is its initial state, and the wave function describes the probability distribution and dynamic behavior of the quantum particle in space. The motion and interaction of quantum particles can be simulated using the time-dependent Schrödinger equation in quantum mechanics. These quantum particles may represent particles such as electrons that exhibit significant quantum effects in nanostructures. Initializing the wave function of the quantum particle is crucial to accurately describe its dynamic evolution and interactions during the simulation, thus ensuring the physical meaning and accuracy of the simulation results. The initialization of macroscopic particles is similar to that of classical particles, but at a larger scale, typically used to describe larger structural units or aggregates. The position R of the i-th macroscopic particle is given by... i (0) and velocity V i (0) represents the initial state, and its behavior is simulated using the macroscopic particle motion equations. These particles may represent micrometer-scale particles or clusters, describing their motion and interactions within the overall structure. Initializing the state of the macroscopic particles ensures that the dynamic behavior and interactions of the large-scale structure can be accurately described during the simulation.

[0055] Within each time step, the states of these particles need to be iteratively updated. For classical particles, their displacement and velocity are updated using the classical particle motion equations. These equations are based on Newton's second law, and the particle's trajectory within each time step is calculated using numerical integration. Classical mechanics is suitable for describing the motion of atoms and molecules at the nanoscale, determining the changes in position and velocity of the particle within each time step by calculating forces and accelerations. For quantum particles, their wavefunction is updated by solving the time-dependent Schrödinger equation. The Schrödinger equation in quantum mechanics describes the evolution of quantum states, and the update of the wavefunction reflects the dynamic changes of the quantum particle within each time step. By numerically solving the Schrödinger equation, the probability distribution and interactions of quantum particles can be obtained, thus accurately describing the influence of quantum effects in nanostructures. For macroscopic particles, their displacement and velocity are updated using macroscopic particle motion equations. These equations are typically based on continuum mechanics or other macroscopic mechanical models, describing the motion and interactions of large-scale structures. Numerical integration methods can be used to calculate the trajectory of macroscopic particles, determining their position and velocity changes within each time step. Macroscopic mechanics methods are suitable for describing structures at the micrometer scale or larger, determining the dynamic behavior of macroscopic particles by calculating forces and accelerations.

[0056] At each time step, the system's interaction potential energy also needs to be calculated. This interaction potential energy includes interactions between various particles, such as van der Waals and electromagnetic forces between classical particles, electron interactions between quantum particles, and contact forces and other mechanical interactions between macroscopic particles. By calculating these interaction potential energies, the total energy E of the system can be determined. total Calculating the interaction potential energy is a crucial step in ensuring the accuracy of the simulation results. By accurately describing the interactions between particles, the true physical state of the system can be obtained. Within each time step Δt, the states of all particles are updated iteratively, and the forces and potential energies are recalculated until the system reaches a stable condition. This process requires repeatedly calculating the current total energy. And the quantum density of states matrix ρ(r). The calculation of the total energy involves the sum of the kinetic and potential energies of all particles, while the quantum density of states matrix describes the distribution and density of quantum states in the system. Through multiple iterations, when the total energy E tota1 The convergence of the quantum density of states matrix ρ(r) indicates that the system has reached a thermodynamically stable state.

[0057] The stability of the total energy indicates that the internal structure of the system has reached a minimum energy state, which is usually the most thermodynamically stable state. At this point, the motion and interactions of all particles are in equilibrium, with no further significant changes. The stability of the quantum density of states matrix means that the probability distribution and interactions of quantum particles have also reached equilibrium, and the quantum states in the system no longer undergo significant changes. This multi-scale simulation method can comprehensively describe the behavior of nanostructures at different scales, ensuring the stability and functionality of the designed nanostructure models in practical applications. The combined simulation of classical particles, quantum particles, and macroscopic particles can not only accurately describe the microscopic effects in nanostructures but also consider the dynamic behavior of macroscopic structures. This method can provide theoretical support and simulation basis for the design and optimization of practical materials, ensuring that the final materials possess excellent performance and stability.

[0058] Example 5: Calculate the current total energy using the following formula.

[0059]

[0060] in, This represents the summation over all classical particles; N is the total number of classical particles; p i Let m be the momentum of the i-th classical particle; i Let V(r) be the mass of the i-th classical particle; i Let ) be the position of the i-th classical particle at position r. i Potential energy at the point; U ij (r i r j Let be the interaction potential energy between the i-th and j-th classical particles; For the summation over all quantum particles; ∈ j Let α be the energy eigenvalue of the j-th quantum particle; j The energy coupling coefficient associated with quantum particles; |ψ j (r j )| 2 For the wave function of the j-th quantum particle at position r j The probability density at that location; To sum over all macroscopic particles; P k M represents the momentum of the k-th macroscopic particle; k V is the mass of the kth macroscopic particle; int (R k ) represents the position R of the k-th macroscopic particle. k Internal interaction potential energy at the location; W kl (R k R l Γ represents the interaction potential energy between the k-th and l-th macroscopic particles; ij(r i , ψ j ) represents the interaction energy between the i-th classical particle and the j-th quantum particle; Ξ km (R k r m ) represents the interaction energy between the k-th macroscopic particle and the m-th classical particle; M represents the number of quantum particles; L represents the number of macroscopic particles; k represents the subscript index; l represents the subscript index.

[0061] Specifically, the first part of the formula involves the kinetic energy, position potential energy, and interaction potential energy between classical particles. The kinetic energy of a classical particle is determined by its momentum p. i and mass m i Decision, passed Kinetic energy is the square of the ratio of a particle's momentum to its mass, representing the energy a particle has as it moves through space. Position potential energy V(r) i ) is the particle at a specific position r i The potential energy at a given location describes the influence of the external potential field on the particle at that position. This part of the potential energy is usually related to the electric field, magnetic field, or other physical fields in which the particle is located. Interaction potential energy U ij (r i r j The energy of interaction between particles i and j is described, including van der Waals forces, electrostatic forces, etc. These interaction potential energies are an important component of the system's total energy, affecting the interactions between particles and the overall stability. The energy calculation for the classical particle part integrates kinetic energy, position potential energy, and interaction potential energy. The total classical particle energy of the system is obtained by summing over all classical particles. The classical particle energy is also multiplied by a correction factor. This factor takes into account the number of times N, the basic unit cell, is replicated in three-dimensional space. x N y and N z And the number of functional group sizes s and the functional group volume V ij This ensures the uniformity of the nanostructure and the rational distribution of functional groups. Secondly, there is the quantum particle component. The energy eigenvalue of each quantum particle ∈ j and the energy coupling coefficient α associated with quantum particles j The energy of a quantum particle is determined by its wave function ψ. j (r j At position r j The probability density at |ψ j (r j )| 2 This reflects the probability of a quantum particle's existence and its energy distribution at that location. The energy of the quantum particle portion is calculated by summing over all quantum particles, yielding its total energy contribution. The energy calculation of a quantum particle includes its energy eigenvalues ​​∈j , representing the intrinsic energy of a quantum state, and the energy coupling coefficient α. j |ψ j (r j )| 2 This describes the probability density and interaction energy of quantum particles in space. Quantum mechanics is applicable to describing the behavior of microscopic particles such as electrons, determining the dynamic behavior and energy distribution of quantum particles through the probability density of the wave function. Then there's the part about macroscopic particles. The kinetic energy of a macroscopic particle is determined by its momentum p. k and quality M k Decision, passed Represented by: Position potential energy V int (R k This describes the macroscopic particle at position R. k The internal interaction potential energy at a given location. The interaction potential energy W between macroscopic particles. kl (R k R l The equation describes the interaction energy between macroscopic particles k and l. These interaction potential energies affect the interactions between macroscopic particles and the overall stability. The energy of the macroscopic particles is summed over all macroscopic particles to obtain the total energy of the system's macroscopic particles. The energy calculation of macroscopic particles includes kinetic energy, position potential energy, and interaction potential energy. These energy terms describe the dynamic behavior and interaction energy of macroscopic particles, and their behavior is simulated using a continuum mechanics model. Finally, the equation also includes the interaction energy Γ between classical particles and quantum particles. ij (r i , ψ j And the interaction energy Ξ between macroscopic particles and classical particles. km (R k r m These interaction terms ensure the energy coupling and mutual influence between different types of particles, thus accurately reflecting the total energy of the entire system. The interaction energy Γ between classical particles and quantum particles. ij (r i , ψ j This describes the interaction between classical and quantum particles in space, determining their interaction energies through wave function coupling. The interaction energy Ξ between macroscopic particles and classical particles is also described. km (R k r mThis method describes the interactions between macroscopic and classical particles in space, determining their interaction energies through a mechanical model. This multi-scale simulation approach comprehensively describes the behavior of nanostructures at different scales, ensuring the stability and functionality of the designed nanostructure models in practical applications. After initializing the state of each type of particle, these states are iteratively updated at each time step, and the interaction potential energy and total energy are calculated until the system reaches a stable condition. At each time step, the state of classical particles is updated using the classical particle equations of motion, the wave function of quantum particles is updated by solving the time-dependent Schrödinger equation, and the state of macroscopic particles is updated using the macroscopic particle equations of motion. The total energy is calculated repeatedly. With the quantum density of states matrix ρ(r), the system gradually tends towards a thermodynamically stable state. The calculation of the total energy involves the sum of the kinetic and potential energies of all particles, while the quantum density of states matrix describes the distribution and density of quantum states in the system. When the total energy E... total The convergence of the quantum density of states matrix ρ(r) indicates that the system has reached a thermodynamically stable state.

[0062] Example 6: Total Model Energy E total The convergence condition is expressed by the following formula:

[0063]

[0064] in, This represents the total energy in the nth iteration. The total energy in the (n+1)th iteration; ΔE is the energy change; ∈ E The energy convergence threshold is a preset positive number; the convergence condition of the quantum state density matrix ρ(r) is expressed by the following formula:

[0065] Δρ=∫|ρ (n+1) (r)-ρ (n) (r)|dr<∈ ρ ;

[0066] Where, ρ (n) (r) is the quantum state density matrix of the nth iteration; ρ (n+1) (r) is the quantum state density matrix of the (n+1)th iteration; Δρ is the change in the density matrix; ∈ ρ The convergence threshold of the density matrix is ​​a preset positive number.

[0067] Specifically, the convergence condition for the total system energy is used to determine whether the system has reached a thermodynamically stable state. By continuously iterating and calculating the change in total energy, the energy difference between different iteration steps can be assessed. When this change is less than a preset convergence threshold, it indicates that the total energy of the system has stabilized and no longer changes significantly. The core of this process lies in gradually updating the states of various particles in the system, including the kinetic energy, potential energy, and interaction energy of classical particles, quantum particles, and macroscopic particles. As the iteration proceeds, the total system energy gradually tends towards the lowest energy state, which is the most thermodynamically stable state. By monitoring the change in total energy, it is possible to effectively determine whether the system has reached thermodynamic equilibrium. Secondly, the convergence condition for the quantum density of states matrix is ​​used to determine whether the quantum states in the system have reached a stable state. The quantum density of states matrix describes the probability distribution of quantum particles in space and their interactions. It is updated by solving the time-dependent Schrödinger equation. In each iteration step, by calculating the change in the quantum density of states matrix, the difference in quantum states between different time steps can be assessed. When this change is less than a preset convergence threshold, it indicates that the quantum state density matrix has stabilized and the quantum state distribution no longer changes significantly. This process ensures that the quantum states in the system gradually reach a quantum equilibrium state, reflecting the dynamic behavior of quantum particles and the stability of their interaction energy.

[0068] Example 7: At each time step, the formulas for updating the displacement and velocity of a classical particle using the classical particle motion equations are as follows:

[0069]

[0070] Where, r i (t) is the position vector of the i-th classical particle at time t; r i (t+Δt) is the position vector of the i-th classical particle at time t+Δt; v i (t) is the velocity vector of the i-th classical particle at time t; v i (t+Δt) is the velocity vector of the i-th classical particle at time t+Δt; Δt is the time step; a i (t) represents the acceleration of the i-th classical particle at time t; b i (t) is the time derivative of the acceleration of the i-th classical particle at time t; γ is the external force acting on the i-th classical particle at time t; i is the external field coupling coefficient, used to describe the interaction strength between the i-th classical particle and the external force field.

[0071] Specifically, in Example 7, the displacement and velocity of the classical particle are updated using the classical particle motion equations. This process incorporates the fundamental principles of Newtonian mechanics and considers higher-order derivative terms and the influence of external forces to improve simulation accuracy and realism. First, the position update formula accurately describes the trajectory of the classical particle by considering velocity, acceleration, and their higher-order derivative terms. In this formula, r... i (t) is the position vector of the i-th classical particle at time t, and r i (t+Δt) is its position vector at time t+Δt. This is achieved by using the velocity term v... i (t)Δt, acceleration term The time derivative of acceleration and external force terms Adding these terms together gives the particle's position at the next time step. Among these terms, the velocity and acceleration terms describe the particle's basic motion, while the higher-order derivative and external force terms consider the details of the particle's motion in complex external force fields, thus improving the accuracy of the simulation. In this position update formula, the velocity term v... i (t)Δt represents the linear displacement of the particle at its current velocity. Acceleration term. This represents the second displacement of the particle under the current acceleration, a term derived from the definition of acceleration in Newton's second law. (Higher-order derivative terms) The variation of acceleration over time was further considered, reflecting the nonlinear change of the particle's trajectory at higher time orders. The external force term... This describes the additional effect of external forces on particle motion, expressed through the external field coupling coefficient γ. i This is used to quantify the strength of the interaction between the particle and the external force field. Thus, by combining these terms, the formula can more accurately predict the particle's motion under complex force fields. Secondly, the velocity update formula accurately calculates the velocity of the classical particle by considering the average change of acceleration and its higher-order derivatives over the time step. In this formula, v... i (t) is the velocity vector of the i-th classical particle at time t, and v i (t+Δt) is its velocity vector at time t+Δt. The formula includes the current acceleration a. i (t) and the acceleration a at the next time step i The average value of (t+Δt) and the average value of the acceleration time derivative term These terms work together to update particle velocities more accurately. The velocity update formula considers the average change in acceleration within a time step, achieved by averaging the acceleration at two time points, ensuring the continuity and accuracy of velocity updates. The inclusion of higher-order derivative terms further improves the formula's accuracy, especially when particle acceleration changes rapidly or is subjected to complex forces; this term captures more dynamic details. Thus, by combining these higher-order terms, the formula can describe not only simple linear motion but also more complex dynamic environments. In this way, the displacement and velocity of classical particles are accurately updated within each time step. This high-precision simulation method is crucial for describing particle motion in nanostructures. Particles in nanostructures are typically affected by various complex force fields, including van der Waals forces and electromagnetic forces, and these force fields often vary significantly with time and spatial location. Therefore, by introducing higher-order derivative terms and external force terms, the motion behavior of particles in nanostructures can be described more comprehensively, ensuring the accuracy and reliability of the simulation results.

[0072] Example 8: When updating the position and velocity of a quantum particle by solving the time-dependent Schrödinger equation, the time-dependent Schrödinger equation is expressed using the following formula:

[0073]

[0074] ψ j (r, t) represents the wave function of the j-th quantum particle at time t and position r. Wave function ψ j (r, t) is the core quantity describing the state of a quantum system, containing all information about the distribution and evolution of particles in space. Planck's constant. It is a fundamental constant in quantum mechanics, and its introduction allows the equations to correctly describe quantum effects. The left side of the equation... This describes the rate of change of the wave function over time, reflecting the time evolution of the quantum state. The first term on the right... It is a kinetic energy operator that describes the motion behavior of particles in space. It is the Laplace operator, representing the second-order partial derivatives of a particle in various directions, reflecting the diffusion and propagation characteristics of the particle. The second term V eff (r j (t) is the effective potential energy, describing the particle's potential energy at position r. j The potential energy experienced at time t. This includes the potential energy from the external potential field and the internal interaction potential energy, reflecting the influence of the particle's environment. Changes in effective potential energy directly affect the shape and evolution of the wave function. The third term g|ψ j (r, t)| 2This is a nonlinear term describing the self-interactions of particles. This is crucial in certain quantum systems (such as Bose-Einstein condensates), where self-interactions lead to attractive or repulsive effects between particles, thus influencing the distribution and evolution of the wave function. The fourth term, ∑... k λ k cos(ω k t)r j ·E k (t) is a time-dependent external field term that describes the behavior of a particle under the influence of an external electric field. Here, λ k It is the coupling coefficient, which quantifies the strength of the interaction between the particle and the external electric field; ω k It is the frequency, which describes the periodic change of the external electric field; E k (t) represents the external electric field at time t. This term reflects the influence of the external electric field on the particle, including periodic oscillations and spatial dependence, thus affecting the particle's motion and the evolution of the wave function. Solving the time-dependent Schrödinger equation requires considering all these interactions and influences. By solving this equation, the evolution of the wave function at any time can be obtained, thus determining the state changes of the quantum particle. In practical calculations, numerical methods are often used to approximate the solution of this equation, such as the time evolution operator method. Through numerical solutions, the wave function can be updated at each time step, yielding the changes in the quantum particle's position and velocity.

[0075] Where, ψ j (r, t) is the wave function of the j-th quantum particle at time t; h is Planck's constant; Let m be the Laplace operator of the j-th quantum particle; j V is the mass of the j-th quantum particle; eff (r j ,t) represents the position of the j-th quantum particle at position r j and the effective potential at time t; g|ψ j (r, t)| 2 The term ∑ represents a nonlinear term describing the self-interaction of quantum particles. k λ k cos(ω k t)r j ·E k (t) represents the time-dependent external field term, where λ k ω is the coupling coefficient. k For frequency, E k (t) represents the external electric field at time t;

[0076] ψ j (r, t+Δt)=U(t+Δt, t)ψ j (r, t);

[0077] Where U(t+Δt, t) is the time evolution operator, expressed by the following formula:

[0078]

[0079] Where V is the kinetic energy part of the Hamiltonian operator; T is the potential energy part of the Hamiltonian operator; and δ is the imaginary number symbol.

[0080] The principle of the time evolution operator is based on the Hamiltonian operator in quantum mechanics. The Hamiltonian operator H includes the total energy of the system, consisting of kinetic and potential energy. During time evolution, the change in the wave function is influenced by both of these energies. The time evolution operator U(t+Δt, t) is approximately represented as the product of three exponential operators, simplifying the calculation by splitting the contributions of kinetic and potential energy. This approximation method is called the split operator method, a commonly used method for numerically solving the time-dependent Schrödinger equation. First, consider the kinetic energy operator. In the first half of the time step, the wave function evolves using the kinetic energy operator, simulating the evolution of particles under the influence of kinetic energy. The kinetic energy operator primarily deals with the diffusion and propagation of particles in space, and its mathematical form includes a second-order differential operator, describing the particle's motion characteristics. Next, we consider the potential energy operator. In the middle of the time step, the wave function is evolved using the potential energy operator, a process that simulates the particle's evolution under the influence of potential energy. The potential energy operator reflects the particle's behavior under the influence of an external potential field and internal interactions, including position-dependent potential energy changes. Finally, the kinetic energy operator is applied again. This completes the second half of the time step. Through this symmetrical splitting method, the wave function is subjected to the combined influence of kinetic and potential energy throughout the entire time step. The advantage of this splitting operator method lies in its numerical stability and computational efficiency. Since the exponential forms of the kinetic and potential energy operators can be handled separately, this method effectively reduces numerical errors and is applicable to most practical calculations. By alternately applying the kinetic and potential energy operators within each time step, the time evolution of the wave function can be accurately simulated, ensuring the physical accuracy of the calculation results. In practical applications, this method allows the wave function of the quantum particle to be updated within each time step, thereby calculating the changes in the particle's position and velocity. This is particularly important for describing the dynamic behavior of complex quantum systems, especially in the design and optimization of nanostructured materials. Through accurate time evolution calculations, we can gain a deeper understanding of the impact of quantum effects on material properties, thereby optimizing the microstructure and macroscopic properties of materials.

[0081] Example 9: The displacement and velocity of macroscopic particles are updated using the following formula based on the equations of motion of macroscopic particles:

[0082]

[0083] Among them, Rk (t) represents the position of the k-th macroscopic particle at time t; R k (t+Δt) represents the position of the k-th macroscopic particle at time t+Δt; V k (t) represents the velocity of the k-th macroscopic particle at time t; V k (t+Δt) is the velocity of the k-th macroscopic particle at time t+Δt; A k (t) represents the acceleration of the k-th macroscopic particle at time t; A k (t+Δt) represents the acceleration of the kth macroscopic particle at time t+Δt.

[0084] Specifically, the position update formula uses the current position, velocity, and acceleration to calculate the position at the next moment. This formula originates from Newton's laws of motion and reflects the smooth motion of a particle in a constant force field. By using the velocity term V... k (t)Δt and acceleration term Adding them together allows for a precise description of the particle's trajectory within a time step Δt. The velocity term V... k (t)Δt represents the linear motion of the particle at its current velocity, while the acceleration term... This describes the secondary displacement of the particle under the current acceleration; this term reflects the additional displacement caused by the change in acceleration. Secondly, the velocity update formula uses the average of the accelerations at the current and next moments to calculate the velocity at the next moment. This formula is also based on Newton's laws of motion; by considering the average change in acceleration over the time step, it can update the particle's velocity more accurately. Current acceleration A k (t) and the acceleration A at the next moment k The average value of (t+Δt) reflects the changing trend of particle acceleration within a time step, ensuring the continuity and accuracy of velocity updates. These equations of motion are crucial in numerical simulations, especially for describing the dynamic behavior of macroscopic particles. These formulas can handle not only simple linear motion but also more complex force fields and motion patterns. In practical applications, these formulas are often used to simulate large-scale particle systems, such as the motion of gas molecules, liquid flow, and the motion of solid particles in external force fields. Through accurate displacement and velocity updates, the trajectories and dynamic behaviors of particles under different conditions can be simulated, thus providing a reliable numerical tool for understanding and predicting the behavior of macroscopic systems.

[0085] The present invention has been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of the invention. The descriptions of the embodiments above are merely for the purpose of helping to understand the method and core ideas of the present invention. It should be noted that those skilled in the art can make various improvements and modifications to the present invention without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A method for preparing a nanostructure-guided self-cleaning radiative cooling material, characterized in that, The method includes: Step 1: The initial nanostructure model of the self-cleaning radiation cooling material is designed as a multi-scale periodic nanocrystal with embedded functional groups of different scales; Step 2: Based on the initial nanostructure model, perform multi-scale simulations using molecular dynamics to minimize the total energy of the model and obtain a stable structure, thus obtaining the nanostructure model at this point. Step 3: Based on the nanostructure model, prepare self-cleaning radiation cooling materials; In step 2: the total volume of the initial nanostructure model is expressed using the following formula: ； in, This represents the total volume of the initial nanostructure model; , and These represent the number of times the basic unit cell is replicated in the X, Y, and Z axes of three-dimensional space, respectively. This represents the total number of scales corresponding to the embedded functional groups; For the first The number of functional groups in each scale; For the first The first of the scales The volume of each functional group; at each scale, the embedded functional group is described and simulated by three types of particles, namely classical particles, quantum particles and macroscopic particles; and All are subscript indexes. The value ranges from 1 to , The value ranges from 1 to ; Step 2 specifically includes: for each embedded functional group at each scale, initializing its first... The positions of the classical particles are The speed is ; Initialize its first The wave function of a quantum particle is ; Initialize its first The positions of the macroscopic particles are The speed is At each time step, the position and velocity of the classical particle are updated using the classical particle motion equations; the position and velocity of the quantum particle are updated by solving the time-dependent Schrödinger equation; and the position and velocity of the macroscopic particle are updated using the macroscopic particle motion equations. The interaction potential energy is calculated. At each time step... Iterate within the model until the total energy of the model is reached. and quantum state density matrix All conditions are met, and the iteration includes: calculating the current total energy. Update the states of all particles and recalculate the forces and potential energies; among which, Let be the position vector of the particle in space. , and These are the components of the position vector on the three coordinate axes; This is the current iteration number. It is a positive integer; Regarding the first The first of the scales Each functional group calculates its current total energy using the following formula. : ； Among them, the summation symbol This represents the summation over all classical particles; This represents the total number of classical particles. For the first The momentum of a classical particle; For the first The mass of a classical particle; For the first The position vectors of a classical particle; For the first A classical particle at position Potential energy at the location; For the first The first classical particle and the second The interaction potential energy between classical particles; summation symbol This represents the summation over all quantum particles; The total number of quantum particles; For the first The energy eigenvalues ​​of individual quantum particles; In order to be with the first The energy coupling coefficient associated with each quantum particle; For the first The wave function of a quantum particle at position Probability density at a given point; summation symbol This represents the summation over all macroscopic particles; The total number of macroscopic particles; For the first The momentum of a macroscopic particle; For the first The mass of a macroscopic particle; For the first A macroscopic particle at position Internal interaction potential energy at the location; For the first The first macroscopic particle and the first The interaction potential energy between macroscopic particles; For the first The position vectors of macroscopic particles; For the first The first classical particle and the second The energy of interaction between quantum particles; For the first The first macroscopic particle and the first The energy of interaction between classical particles; , and These are all subscript indices of classical particles, with values ​​ranging from 1 to... ; The subscript index of the quantum particle, with values ​​ranging from 1 to... ; and These are all subscript indices of macroscopic particles, with values ​​ranging from 1 to... .

2. The method for preparing the nanostructure-guided self-cleaning radiation cooling material as described in claim 1, characterized in that, Step 1 specifically includes: defining the size and volume of the basic unit cell; embedding multiple functional groups at various scales into the basic unit cell, with each functional group having its volume calculated based on its geometry; replicating the basic unit cell in three-dimensional space to form a periodic structure; and calculating the total volume of the initial nanostructure model to ensure consistency of the structure at each scale and the periodic boundary conditions.

3. The method for preparing the nanostructure-guided self-cleaning radiation cooling material as described in claim 2, characterized in that, Total energy of the model The convergence condition is expressed by the following formula: ； in, For the first Total energy of each iteration; For the first Total energy of each iteration; Energy change; The energy convergence threshold is a preset positive number; the quantum state density matrix... The convergence condition is expressed by the following formula: ； in, For the first The quantum state density matrix of the next iteration; For the first The quantum state density matrix of the next iteration; This represents the change in the density matrix; This is the convergence threshold of the density matrix, and it is a preset positive number.

4. The method for preparing the nanostructure-guided self-cleaning radiation cooling material as described in claim 3, characterized in that, At each time step, the formulas for updating the displacement and velocity of a classical particle using the classical particle motion equations are as follows: ； ； in, For the first A classical particle in time Position vector at any given time; For the first A classical particle in time Position vector at any given time; For the first A classical particle in time The velocity vector at any given moment; For the first A classical particle in time The velocity vector at any given moment; For time step; For the first A classical particle in time Acceleration at any moment; For the first A classical particle in time The time derivative of the acceleration at time t; For the first A classical particle in time The external forces that are constantly applied; The external field coupling coefficient is used to describe the first... The strength of the interaction between a classical particle and an external force field.

5. The method for preparing the nanostructure-guided self-cleaning radiation cooling material as described in claim 4, characterized in that, When updating the position and velocity of a quantum particle by solving the time-dependent Schrödinger equation, the time-dependent Schrödinger equation is expressed as follows: ； in, For the first A quantum particle in time The wave function; It is Planck's constant; For the first The Laplace operator for a quantum particle; For the first The mass of a quantum particle; For the first A quantum particle at position and time The effective potential of the position; This is a nonlinear term that describes the self-interaction of quantum particles; For time-dependent external terms, where, The coupling coefficient is... For frequency, For time External electric field at that time; ； in, For time evolution operators, the following formula is used: ； in, This represents the kinetic energy component of the Hamiltonian operator; This represents the potential energy component of the Hamiltonian operator; It is the symbol for imaginary numbers.

6. The method for preparing the nanostructure-guided self-cleaning radiation cooling material as described in claim 5, characterized in that, The displacement and velocity of macroscopic particles are updated using the following formula based on the equations of motion of macroscopic particles: ； ； in, For the first A macroscopic particle in The position at that moment; For the first A macroscopic particle in The position at that moment; For the first A macroscopic particle in The speed of time; For the first A macroscopic particle in The speed of time; For the first A macroscopic particle in Acceleration at any moment; For the first A macroscopic particle in Acceleration at any moment.

Images