Modeling and simulation method for fractal growth of surface morphology of nano-silver flexible film

Abstract

The application discloses a modeling and simulation method for surface morphology fractal growth of a nano-silver flexible film, and steps are as follows: 1, establishing a nano-silver flexible film surface morphology fractal growth model conforming to the surface morphology fractal growth of the nano-silver flexible film; 2, calibrating parameters of the model according to electron microscope scanning image data of the nano-silver flexible film obtained through experiments; and 3, verifying effectiveness and applicability of the model for simulating the surface morphology fractal growth of the nano-silver flexible film by using a morphology fractal dimension measurement technology.The model for the surface morphology fractal growth of the nano-silver flexible film can quickly simulate the surface morphology growth process of the nano-silver flexible film prepared by an in-situ reduction method, and can simulate the surface morphology fractal growth process of the film under different silver ion concentrations and reduction reaction time parameters.The simulation result of the model can guide experimental research on preparation of the nano-metal flexible film and accelerate the optimization speed of the preparation process.

Description

Technical Field

[0001] This invention relates to the field of novel flexible nanomaterials, and mainly to a modeling method for the growth of surface morphology of novel flexible nanomaterials, particularly to a fractal growth modeling method for the surface morphology of flexible silver nanofilms. Background Technology

[0002] Polyimide polymers contain a large number of aromatic backbones, thus polyimide films, especially fully aromatic polyimide films, exhibit excellent thermal stability. This characteristic makes polyimide films a promising candidate for applications in flexible electronics, including microelectronic packaging, flexible displays, flexible printed circuit boards, and flexible solar cells. Furthermore, nanomaterials possess both metallic properties and unique nano-effects, allowing for diverse applications depending on their morphology and structure. Combining nanomaterials with specific morphologies into flexible polyimide films allows for the fabrication of various functionalized flexible electronic device substrates, further enhancing the functionality of flexible electronic devices and expanding their application areas.

[0003] Silver / polyimide composite films are a type of flexible nano-metal composite film. Since the introduction of this film preparation process using ion exchange and in-situ growth, related research on silver / polyimide composite films with different functions has been successively proposed. The function and performance of the nano-silver polyimide composite film are determined by the surface morphology of the film, and the preparation process of the composite film directly determines the surface morphology of the metal composite film. Currently, the reported surface morphologies of nano-silver polyimide composite films include granular, linear, and dendritic structures. The early preparation process mainly consisted of two steps: the first step was to synthesize nano-silver metal materials with special morphologies, and the second step was to coat or print coatings and inks containing nano-silver metals onto the polyimide film. This two-step process has the following two problems: First, the synthesis of coatings or inks containing nano-silver metal materials will significantly increase the resistivity of the conductive layer of the final composite film; second, the process of combining coatings or inks with flexible substrates may cause the conductive layer to detach during actual application of the composite film, that is, the adhesion strength between the conductive layer and the flexible film is weak, which is also the most serious problem in the existing process.

[0004] To address these two issues, in recent years, scholars both domestically and internationally have attempted to use in-situ growth processes to directly grow silver nanomaterials on the surface of flexible polyimide polymer films, hoping to simplify the preparation process of silver nanomaterial composite films while improving the adhesion strength between silver and polyimide films. The most widely studied process for in-situ growth of silver nanomaterials is electrodeposition, where a metal salt solution can be directly deposited onto the film surface to form a nanomaterial layer with a special structure under the presence of an electric field. However, electrodeposition requires adding a step of electrodepositing nanomaterials to the existing mature polymer film preparation process. Furthermore, current electrodeposition methods are mostly implemented on ITO films, which are relatively expensive, and the substrates are mostly glass, thus limiting the development of this technology in the application of flexible conductive films.

[0005] To address the problems associated with in-situ electrodeposition methods, researchers have proposed a scheme to prepare flexible silver nanoparticle composite films on the surface of flexible polyimide films using in-situ reduction. These schemes grow a conductive silver film on the surface of commercially available polyimide films through a simple chemical reaction. Because silver ions enter the polymer film during ion exchange loading, the in-situ reduced silver nanoparticles exhibit high adhesion strength to the film. This in-situ reduction method for preparing flexible silver nanoparticle polyimide films is of great research and practical application significance, not only for simplifying the fabrication process of nano-metal composite films but also for significantly improving the overall quality of functional nano-metal composite films.

[0006] The in-situ reduction method for preparing flexible silver nanofilms described in the aforementioned study is still immature and in the laboratory research stage. Several factors during the preparation process, such as the concentration of AgNO3 solution, KOH solution, and silver ion reduction reaction time, can affect the surface morphology of the nano-metal composite film and its final performance and properties. To optimize the preparation process and obtain a high-performance flexible silver nanofilm, various process parameters need to be continuously adjusted during the preparation experiments. However, each parameter adjustment requires repeating the film preparation process, resulting in very low time efficiency in laboratory research. If a growth model of the silver nanofilm can be established using computer simulation technology, the optimization speed of the preparation process can be accelerated, which in turn can guide experimental research on the preparation of flexible silver nanofilms and improve the efficiency of laboratory research.

[0007] In recent years, computer simulation technology has yielded significant results in the research of thin film material growth simulation. For example, some scholars have used machine learning, artificial neural networks, and deep learning techniques to establish process parameter optimization models for thin film process parameter optimization; others have used first-principles calculations and kinetic Monte Carlo methods to establish growth models to study the growth and kinetic processes of metal composite films. These parameter optimization models do not involve the thin film process flow or the growth principle of nano-metal thin films; the model input consists of various process parameters, and the model output is the thin film performance parameters of interest. A large amount of experimental data is used as training samples to train the parameter optimization model and optimize the thin film preparation process. Thin film growth model research methods, on the other hand, require a specific thin film preparation process flow and a clear understanding of the specific details and growth mechanisms of nano-metal thin film surface growth. Currently, research on the preparation of nano-silver polyimide composite films using in-situ reduction methods is still in its early stages both domestically and internationally. Therefore, there is still a lack of experimental research that can guide thin film preparation and a growth model capable of rapidly simulating the surface morphology of nano-silver thin films. Summary of the Invention

[0008] To address the shortcomings of existing technologies, this invention proposes a fractal growth modeling method for the surface morphology of flexible silver nanofilms based on an in-situ reduction preparation process.

[0009] The technical solution provided by this invention is as follows:

[0010] A fractal growth modeling and simulation method for the surface morphology of flexible silver nanofilms is presented, with the following steps:

[0011] Step 1: Establish a surface deposition model that conforms to the fractal growth of the surface morphology of flexible silver nanofilms based on the in-situ reduction method.

[0012] Step 2: Based on the electron microscopy scan image of the flexible silver nanofilm, the reduction reaction time and silver ion concentration are respectively correlated with the particle concentration and reaction time of the surface deposition model. Then, the particle concentration and reaction time of the surface deposition model are calibrated to establish a fractal growth model of the surface morphology of the flexible silver nanofilm.

[0013] Step 3: By comparing the experimental preparation results and the model simulation results, the accuracy and applicability of the fractal growth model of the surface morphology of the flexible silver nanofilm calibrated with the experimental preparation parameters are verified.

[0014] Furthermore, in step 1 of the method, the steps for establishing the surface deposition model are as follows:

[0015] (1) Define a seed plane for a flexible substrate that simulates a nanosilver film. The growth process of the particles starts from this plane, and these particles are used as seed particles.

[0016] (2) A particle is randomly generated near the circumference at a certain distance from each seed particle. The particle performs Brownian motion to simulate random walking. When the distance between the particle and the seed particle is less than the cohesion distance, the particle attaches to the seed particle to form a particle cluster, and the particle cluster is defined to replace the original seed particle. If the distance between the particle and the seed particle exceeds the escape radius, it is considered abandoned and no longer performs random movement. The generation and random walking process of random particles are repeated continuously, and new particle clusters are continuously generated.

[0017] (3) As the random process and simulation time increase, eventually many particles will form several large particle clusters, which reflect the surface morphology of the nanosilver flexible film.

[0018] Furthermore, in step 1, the space of the surface deposition model is defined as a bounded space.

[0019] Furthermore, in step 1, the surface deposition model space is a cube, and the initialization parameters include the total number of particles N, the substrate side length L, the film deposition space height H, and the minimum number of clusters N. min Particle diameter and adhesion distance d0, Brownian motion step size step, deposition rate drop, and plotting step size; where the minimum cluster number N min The minimum number of clusters that determine complete reaction in the model is represented by the drawing step size, which represents the number of random Brownian motions during one drawing operation.

[0020] Furthermore, in step 1, the three-dimensional spatial coordinates of each particle and its cluster information are stored in a structure, where X, Y, and Z represent the spatial coordinate components of each particle, and the cluster number Num records the cluster to which the particle belongs; the particle undergoes downward deposition motion while performing random Brownian motion.

[0021] Furthermore, in step 2, the method for calibrating the silver ion concentration parameter is to convert the silver ion concentration during the preparation process into the number of particles in the spatial volume of the established fractal growth model. The specific calibration steps are as follows:

[0022] ① Define the model space as a cube with height H and a square base with side length L; the base of this square corresponds to the flexible substrate of the silver nanofilm, with a base area of ​​L. 2 ;

[0023] ② Set the number of particles in the model space to N, which corresponds to the silver ion concentration parameter;

[0024] ③Based on the known silver ion concentration parameter m, the scanning electron microscope image of the nano-silver flexible film sample prepared experimentally was used to extract a square region with a side length of l, and the number of silver ions n in the square region was calculated using image processing methods.

[0025] ④ According to L 2 : 2 =:n, Repeat step ③ to obtain the silver ion concentration parameter m and model parameter r from the scanning electron microscope images of thin film samples with different silver ion concentration parameters. 2 The correspondence between / N;

[0026] ⑤ In the model, the particle radius and the total number of particles N are fixed. As the simulated silver ion concentration parameter m changes, the side length L of the model space changes accordingly based on the correspondence between m and the model parameter r obtained in step ④.

[0027] Furthermore, in step 2, as the reaction time increases, the thickness of the flexible film increases, which corresponds to a longer model running time and an increase in the height H of the model space. The specific calibration steps are as follows:

[0028] ① Based on the experimental preparation and measurement, a set of experimental data on reaction time and film thickness were obtained. The corresponding relationship between reaction time t and film thickness parameter D was obtained by computer fitting method. During calibration, film thickness D was calculated based on unit film thickness sd. That is, if the actual film thickness is d, then film thickness parameter D = d / sd.

[0029] ② In the model, the ratio a = H / sd between the height H of the model space and the unit film thickness sd is fixed; when the reaction time t to be simulated changes, the height H of the model space can be obtained by multiplying the correspondence between the reaction time t and the film thickness parameter D by the ratio a.

[0030] Furthermore, in step 3, the model validation method consists of the following steps:

[0031] ① By changing the silver ion concentration and reduction reaction time, two preparation parameters were modified through experimental preparation methods to obtain flexible silver nanofilm samples with different preparation parameters;

[0032] ② Scanning electron microscopy (SEM) images of flexible silver nanofilm samples under different preparation parameters were obtained.

[0033] ③ Using electron microscopy scan images of flexible silver nanofilm samples, fractal dimension calculation methods were used to obtain fractal dimension parameters that can characterize the surface morphology of flexible silver nanofilm samples under different preparation parameters.

[0034] ④ Using the same preparation parameters as in ①, set the particle concentration and reaction time parameters in the surface morphology fractal growth model respectively, and obtain the model simulation results under different parameters;

[0035] ⑤ The simulation results of the model are processed into two dimensions, and the fractal dimension calculation method is used to obtain the fractal dimension parameters that characterize the surface morphology of the thin film in the model simulation.

[0036] ⑥ Compare and analyze the fractal parameters calculated in ③ and ⑤ under different parameters to verify the accuracy and applicability of the established fractal growth model of the surface morphology of flexible silver nanofilm.

[0037] Relevant modeling principles:

[0038] Based on the fundamental principle of in-situ metal growth on the surface of polyimide films, the preparation process of flexible silver nanofilms using the in-situ reduction method mainly includes three steps: hydrolysis of the polyimide polymer film surface to form polyamate; replacement of the original silver ions in the polyamate with silver ions in a silver ammonia solution to form a silver-loaded film; and reduction of the silver-loaded film in a reducing agent followed by surface deposition to form the flexible silver nanofilm. Experimental results show that the concentration of silver ions in the silver ammonia solution and the reduction reaction time are the main factors affecting the surface morphology of the flexible silver nanofilm. Furthermore, the preparation process of the flexible silver nanofilm shows that the growth of the silver nanofilm is completed on a planar substrate; therefore, its fractal growth process is surface-centric, making it suitable for modeling its fractal growth process based on a surface deposition model.

[0039] The beneficial effects of this invention are as follows:

[0040] (1) The method provided by the present invention can run computer simulation calculations to quickly simulate the surface morphology of nano-silver flexible thin films based on the in-situ reduction method preparation process;

[0041] (2) This invention can simulate and model the fractal growth of the surface morphology of flexible silver nanofilms under different preparation process parameters by changing the model parameters;

[0042] (3) This invention can guide experimental research on the preparation of flexible nano-metal films through model simulation results, accelerate the optimization of the preparation process, and thus improve the work efficiency of laboratory research. Attached Figure Description

[0043] Figure 1 This is a flowchart of the fractal growth modeling method for the surface morphology of flexible silver nanofilms based on the in-situ reduction method according to an embodiment of the present invention.

[0044] Figure 2 This is a flowchart illustrating the fractal growth process of the simulated surface morphology of a flexible nanosilver film according to an embodiment of the present invention.

[0045] Figure 3a This is a flowchart of the silver ion concentration parameter calibration process in the model of this embodiment of the invention; Figure 3bThis is a flowchart of the reaction time parameter calibration process in the model of this invention embodiment.

[0046] Figure 4 This is a flowchart of the model verification method according to an embodiment of the present invention.

[0047] Figure 5 This is a diagram simulating the fractal growth process of the surface morphology of a flexible silver nanofilm in an embodiment of the present invention. In the diagram, St and n represent the number of random motion steps and the number of clusters, respectively.

[0048] Figure 6 These are images showing the fractal growth results of the simulated surface morphology of a flexible silver nanofilm in an embodiment of the present invention, along with a comparison image of the experimental sample using scanning electron microscopy.

[0049] Figure 7 This is a comparison chart of the fractal dimension calculation results of the experimental sample morphology and the model simulation morphology in the embodiments of the present invention. Detailed Implementation

[0050] The technical solution of the present invention will be further described in detail below through embodiments and in conjunction with the accompanying drawings.

[0051] In experimental research on flexible silver nanofilms prepared using the in-situ reduction method, when it is necessary to optimize the process parameters for film preparation, the fractal growth model of the surface morphology of the flexible silver nanofilm obtained through the three steps of this invention can be used. By applying computer simulation technology and changing the model parameters, the fractal growth process of the film surface morphology can be simulated, accelerating the acquisition of the surface morphology characteristics of the film under different preparation process parameters. This provides a basis for guiding the optimization of film preparation process parameters and ensures improved work efficiency in laboratory research.

[0052] Example

[0053] I. Relevant Theories Involved in This Invention

[0054] The basic principle of in-situ metal growth on polyimide film surfaces is as follows: First, an alkaline metal solution is used to break the imide rings within the polyimide polymer, causing it to hydrolyze into polyamic acid. Metal ions from the alkaline solution then replace the hydrogen ions ionized from the carboxyl groups, forming a polyamic acid salt with metal ions. Subsequently, the polyamic acid salt with metal ions is immersed in a silver ammonia solution. Based on the principle of preferential substitution of smaller ions in ion exchange, the silver ions in the silver ammonia solution replace the silver ions in the original polyamic acid salt, thus loading the film with silver ions. Finally, the silver-loaded film is placed in a reducing agent, where the silver ions are directly reduced to elemental silver on the film surface. This step is also known as the in-situ growth process. Studies have found that during the in-situ growth process, when the polyamic acid-silver film is immersed in a reducing agent solution, a nanoparticle-like silver layer is obtained.

[0055] Based on this, this invention proposes and implements a fractal growth modeling method for the surface morphology of flexible silver nanofilms based on an in-situ reduction method. This method uses a single particle in physical space to represent a single silver ion. First, a seed plane is defined to simulate the flexible substrate of the silver nanofilm. The particle growth process begins from this plane, and these particles serve as seed particles. A particle is randomly generated near the circumference of each seed particle at a certain distance. This particle undergoes Brownian motion to simulate random movement. When the distance between this particle and the seed particle is less than the aggregation distance, it ceases random movement and attaches to the seed particle to form a particle cluster, which replaces the original seed particle. If the distance between this particle and the seed particle exceeds the escape radius, it is considered discarded and stops random movement. The generation and random movement of random particles are repeated continuously, constantly generating new particle clusters. As the random process and simulation time increase, eventually, numerous particles will form several large particle clusters, reflecting the surface morphology of the flexible silver nanofilm. The modeling process fully considered the effects of silver ion concentration in the silver ammonia solution and the reduction reaction time on the surface morphology of the flexible silver nanofilm, and the model parameters were calibrated using experimental data. This facilitates quantitative research on the optimization of film preparation process parameters.

[0056] II. Specific Implementation Steps

[0057] As attached Figure 1 As shown, the steps are as follows:

[0058] (1) Based on the fundamental principle of in-situ metal growth on the surface of polyimide films and the fabrication process of flexible silver nanofilms, a surface deposition model for fractal growth of the surface morphology of flexible silver nanofilms was established. The specific establishment process of the example is attached. Figure 2 As shown, the specific process is described below:

[0059] ① The initialization parameters in the surface deposition model include the total number of particles N, the substrate edge length L, the film deposition space height H, and the minimum number of clusters N. min Particle diameter and adhesion distance d0, Brownian motion step size step, deposition rate drop, plotting step size.

[0060] The total number of particles N is the total number of particles generated at once in space in the simulation of the surface deposition model. All particles are processed in parallel. The larger the number of particles N is, the greater the amount of computation required and the longer the simulation time, but the simulation results will be more obvious. In this example, the total number of particles N is set to 5000.

[0061] The two parameters, substrate edge length L and film deposition space height H, are used to characterize the flexible substrate edge length and reaction rate of the silver nanofilm.

[0062] Minimum number of clusters N minThis refers to the process of surface deposition, in which more and more individual particles join the clusters as the simulation time increases, and the clusters will also collide and merge, resulting in fewer and fewer clusters. In this embodiment, this parameter is set to 60.

[0063] In the model, each particle represents a silver ion. The particles are considered to be uniform spheres with consistent size. The diameter of a silver ion was experimentally measured to be 29 nm. Therefore, in this embodiment, the particle diameter and adhesion distance d0 parameters are set to 1, and the unit length in the simulated spatial coordinate system is equivalent to the actual 29 nm. This will serve as an important benchmark for the subsequent calibration of the model's spatial dimensions L and H. At the same time, the particles undergo Brownian motion under the impact of molecular thermal motion in the solution. This random motion causes the particles to collide with each other and aggregate. When the distance between the centers of two particles is equal to the particle diameter, the two particles can be considered to be adhered together.

[0064] When a particle is in a solution, it undergoes Brownian motion due to collisions with liquid molecules from all directions caused by the thermal motion of the liquid molecules. The distance the particle travels each time is the step size of the Brownian motion, which is set to 0.75d0 in this embodiment.

[0065] The deposition rate drop is used to characterize the rate at which particles and clusters are deposited toward the substrate in a surface deposition model. In this embodiment, this parameter is set to 0.15d0.

[0066] In simulating the fractal production process of thin films, it is essential to be able to display particle positions using plotting to observe the dynamic process of cluster formation in real time. Since the model processes a large number of particles each time, plotting after each random movement would slow down the simulation. Furthermore, the coordinate changes of the particles after each random movement are not significant. Therefore, considering the need to improve the efficiency of the simulation and the observation effect of fractal growth, this embodiment sets the plotting step size to 10, meaning that plotting is performed once every 10 random movements.

[0067] ② Check whether the total number of clusters is greater than the minimum number of clusters N. min If the value is less than 0, the simulation process ends and the final simulated growth result is plotted; otherwise, the random process of particles and clusters begins.

[0068] ③ At the start of the simulation, initial particles and clusters are generated. Specifically, an N*4 coordinate matrix is ​​created with the total number of particles N as the parameter to store information for all particles. Each row of the matrix represents a particle, with the first three elements set as the particle's x, y, and z coordinates, respectively. The fourth column of the matrix is ​​set from 1 to N as the initial cluster number. The initial coordinates of each particle are generated using a random function, where the x and y coordinates range from 0 to L, and the z coordinate ranges from 0 to H.

[0069] ④ Subsequently, each simulation of the random process of particles and clusters assumes that the particles diffuse in the solution and undergo Brownian motion. In process ③ of this embodiment, each random particle already has its own spatial coordinates (x, y, z) and initial cluster number. Assuming that the particle's step size is equal each time, the next possible position of the particle is a random position on the surface of a sphere with the current position as the center and the step size as the radius. Two random angle parameters, α and β, are generated using a random function, with α and β taking values ​​in [0, 2π] and [0, π], respectively. After random motion, the particle's new coordinates are (x', y', z'), and the formula for calculating the new coordinates is shown in Equation 1. Here, step is the Brownian motion step size.

[0070]

[0071] ⑤ Next, the downward deposition effect of particles and clusters is simulated. In this embodiment, it is assumed that the deposition velocities of particles and clusters moving towards the substrate are the same, satisfying uniform motion. The new coordinates of particles and clusters under the influence of the deposition effect are (x”, y”, z”), and the calculation formula for the new coordinates is shown in Equation 2. Where drop is the deposition rate.

[0072]

[0073] ⑥ Each time a particle undergoes Brownian motion and deposition, it may move to the vicinity of a cluster or go out of bounds. Therefore, after each Brownian motion, a determination of whether the particle has adhered or gone out of bounds must be made. In this embodiment, the determination of whether the particle has adhered is made first, followed by the determination of whether it has gone out of bounds. If a new cluster appears, the cluster number of the particles belonging to that cluster is modified, and the center coordinates of the new cluster are recalculated. The center coordinates of the new cluster are obtained by calculating the centroid of the coordinates of all the particles that make up the cluster. If a cluster is detected to be in contact with the spatial boundary, including the bottom, the four sides, etc., then the cluster is restricted from undergoing random Brownian motion.

[0074] ⑦ Check if the drawing requirements are met, i.e., check if the drawing step size requirement is met. If it is met, draw the current simulated growth result; otherwise, return to process ②.

[0075] Based on the structural characteristics of the active layer of the Thz QCL, the corresponding electron rate equation and photon rate equation are established.

[0076] (2) Based on the surface deposition model that conforms to the fractal growth of the surface morphology of flexible silver nanofilm established in step (1), the two important preparation parameters of reduction reaction time and silver ion concentration are reflected in the two parameters of model substrate side length L and film deposition space height H of the surface deposition model established in step (1) according to the electron microscopy scanning image of the flexible silver nanofilm obtained in the experiment. Based on the experimental preparation data, the two parameters of particle concentration and reaction time of the surface deposition model established in step (1) are calibrated to establish the fractal growth model of the surface morphology of flexible silver nanofilm.

[0077] The model calibration process for the silver ion concentration parameter in this embodiment is as follows: Figure 3a As shown, the specific process is described below:

[0078] ① Multiple flexible silver nanofilm samples were prepared by changing the concentration of silver ammonia solution using experimental preparation methods. In this example, the concentration of silver ammonia solution was set to 0.02 mol / L, 0.04 mol / L and 0.06 mol / L respectively.

[0079] ② Two-dimensional scanning electron microscope images of flexible silver nanofilm samples with three concentrations of silver ammonia solution obtained in process ①.

[0080] ③ A 476*476 pixel square region was cropped from the middle part of the two-dimensional scanning electron microscope (SEM) images of the flexible silver nanofilm samples with three silver ammonia solution concentrations; the ratio of pixels to actual length was obtained according to the scale bar of the SEM image. In this embodiment, 68 pixels correspond to an actual length of 50 μm; the pixel area covered by silver ions was calculated using image processing methods, and the coverage area of ​​silver ions in the cropped square region was calculated according to the ratio of pixels to actual length; finally, the number n of silver ions in the square region was calculated according to the theoretical diameter of silver ions.

[0081] ④ Use parameter fitting methods to obtain the silver ion concentration parameter m and the model parameter r = L 2 The correspondence between / and N. In this embodiment, m is taken as three concentration values: 0.02 mol / L, 0.04 mol / L, and 0.06 mol / L; N is the total number of particles in the model, and in this embodiment, N = 5000.

[0082] ⑤ Based on the model parameter r = L 2 / N, obtain the correspondence between the silver ion concentration parameter m and the model parameter L.

[0083] Furthermore, the model calibration process for the reaction time parameter in this embodiment is as follows: Figure 3b As shown, the specific process is described below:

[0084] ① By changing the reduction reaction time parameters using experimental preparation methods, multiple flexible silver nanofilm samples were prepared. In this embodiment, the reduction reaction time was set to three values: 30 minutes, 60 minutes, and 90 minutes.

[0085] ② Experimental method: The thickness d of the nanosilver film of the nanosilver flexible film samples with three different reduction reaction times in process ① was measured.

[0086] ③ Define the unit film thickness parameter sd, sd = 100 nm. Based on the actual thickness d data of the silver nanofilm obtained in process ②, calculate the thickness parameter D of the silver nanofilm for each sample, D = d / sd. Use the parameter fitting method to obtain the correspondence between the reduction reaction time t and the silver nanofilm thickness parameter D.

[0087] ④ Based on the model parameter H = a × sd, obtain the correspondence between the reduction reaction time parameter t and the model parameter H. In this embodiment, parameter a = 10. 6 .

[0088] (3) Verify the accuracy and applicability of the fractal growth model of the surface morphology of the flexible silver nanofilm established after parameter calibration in step (2). The model verification process in this embodiment is as follows: Figure 4 As shown, the specific process is described below:

[0089] ① First, through experimental preparation methods, the silver ion concentration and reduction reaction time were varied to obtain 10 sets of flexible silver nanofilm samples under different preparation parameters. The 10 sets of preparation parameters are shown in the table below:

[0090] Group number 1 2 3 4 5 6 7 8 9 10 Silver ion concentration (mol / L) 0.02 0.02 0.02 0.02 0.04 0.04 0.04 0.04 0.06 0.06 Reduction reaction time (minutes) 30 40 60 90 30 40 60 90 30 40

[0091] ② Scanning electron microscopy (SEM) images of 10 sets of nanosilver flexible thin film samples under different preparation parameters were obtained.

[0092] ③ The fractal dimension of the flexible silver nanofilm sample was obtained by using the fractal dimension calculation method to obtain the fractal dimension that can characterize the surface morphology of the flexible silver nanofilm sample under 10 sets of preparation parameters.

[0093] ④ Using the 10 identical sets of preparation parameters from ① as model parameters, a computer was used to calculate the parameters according to the attached... Figure 2 The simulation process is carried out in the simulation.

[0094] ⑤ The three-dimensional spatial coordinate data of particle clusters obtained from the simulation of the 10 models were processed into two dimensions to generate two-dimensional morphology data with the substrate as the plane. Then, the fractal dimension calculation method was used to obtain the fractal dimension of the two-dimensional morphology obtained from the simulation of the model.

[0095] ⑥ The fractal dimensions calculated in ③ and ⑤ under 10 sets of parameters are compared and analyzed to verify the accuracy and applicability of the established fractal growth model of the surface morphology of flexible nanosilver films.

[0096] The surface morphology formation process of nano-silver thin films under the preparation parameters of a silver ion concentration of 0.02 mol / L and a reduction reaction time of 30 min were simulated using the method of this invention. (See attached image) Figure 5 Figures (a), (b), and (c) illustrate the morphological formation process, where St and n represent the number of random motion steps and the number of clusters, respectively. (Appendix) Figure 6 Figures (a), (b), and (c) show the simulated three-dimensional results, two-dimensional simulation results, and electron micrographs of the experimentally prepared samples, respectively. (Attached) Figure 7 (a) and (b) are the calculated fractal dimension results of the experimental sample morphology and the model simulation morphology in the embodiments of the present invention. In the figures, parameter D is the fractal dimension value, and the fractal dimensions of the two are 1.99 and 1.93, respectively, which are very close. It can be seen that the fractal growth model of the surface morphology of flexible silver nanofilm established by the method of the present invention can rapidly simulate the surface morphology growth process of flexible silver nanofilm prepared by in-situ reduction method; and by changing the model parameters, the fractal growth process of film surface morphology under different silver ion concentrations and reduction reaction time parameters can be simulated.

[0097] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

[0098] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the invention.

Claims

1. A method for fractal growth modeling and simulation of surface morphology of flexible silver nanofilms, characterized in that, The steps are as follows: Step 1: Establish a surface deposition model that conforms to the fractal growth of the surface morphology of flexible silver nanofilms based on the in-situ reduction method. Step 2: Based on the electron microscopy scan image of the flexible silver nanofilm, the silver ion concentration and reduction reaction time are respectively correlated with the particle concentration and reaction time of the surface deposition model. Then, the particle concentration and reaction time of the surface deposition model are calibrated to establish a fractal growth model of the surface morphology of the flexible silver nanofilm. The calibration method for the silver ion concentration parameter is to convert the silver ion concentration during the preparation process into the number of particles in the spatial volume of the established fractal growth model. The specific calibration steps are as follows: ① Define the model space as a cube with height H and a square base with side length L; the base of this square corresponds to the flexible substrate of the silver nanofilm, with a base area of... ; ② Set the number of particles in the model space to N, which corresponds to the silver ion concentration parameter; ③Based on the known silver ion concentration parameter m, a scanning electron microscope image of a flexible silver nanofilm sample prepared experimentally was taken, and a section with a side length of... l The number of silver ions, n, in a square region is calculated using image processing methods. ④According to Repeat step ③ to obtain the silver ion concentration parameter m and the model parameter r from the scanning electron microscope images of thin film samples with different silver ion concentration parameters. The correspondence between them; ⑤ In the model, the particle radius and the total number of particles N are fixed. As the simulated silver ion concentration parameter m changes, the side length L of the model space changes accordingly based on the correspondence between m and the model parameter r obtained in step ④. In step 2, as the reaction time increases, the thickness of the flexible film increases, which corresponds to a longer model running time and an increase in the height H of the model space. The specific calibration steps are as follows: ① Based on the experimental preparation and measurement, a set of experimental data on reaction time and film thickness was obtained, and the reaction time was obtained using a computer fitting method. t The correspondence with the film thickness parameter D; during calibration, the film thickness D is calculated based on the unit film thickness sd, that is, if the actual film thickness is d, then the film thickness parameter... ; ② The ratio between the height H of the model space and the unit film thickness sd in the model. Fixed; when the reaction time to be simulated is required. t When changes occur, only reaction time is needed. t The correspondence between the film thickness parameter D and the ratio is then multiplied. a The height H of the model space can then be obtained; Step 3: By comparing the experimental preparation results and the model simulation results, the accuracy and applicability of the fractal growth model of the surface morphology of the flexible silver nanofilm calibrated with the experimental preparation parameters are verified.

2. The method for fractal growth modeling and simulation of the surface morphology of flexible silver nanofilms according to claim 1, characterized in that, In step 1 of the method, the steps for establishing the surface deposition model are as follows: (1) Define a seed plane for a flexible substrate that simulates a nanosilver film. The growth process of the particles starts from this plane, and these particles are used as seed particles. (2) A particle is randomly generated near the circumference at a certain distance from each seed particle. The particle performs Brownian motion to simulate random walking. When the distance between the particle and the seed particle is less than the cohesion distance, the particle attaches to the seed particle to form a particle cluster, and the particle cluster is defined to replace the original seed particle. If the distance between the particle and the seed particle exceeds the escape radius, it is considered abandoned and no longer performs random motion. The generation of random particles and the random walking process are repeated continuously, and new particle clusters are continuously generated. (3) As the random process and simulation time increase, eventually many particles will form several large particle clusters and reach the critical number of particle clusters, which reflects the surface morphology of the nanosilver flexible film.

3. The method according to claim 2, characterized in that: In step 1, the space of the surface deposition model is defined as a bounded space.

4. The method according to claim 2, characterized in that: In step 1, the surface deposition model space is a cube, and the initialization parameters include the total number of particles. N Base side length L Thin film deposition space height H、 Minimum number of clusters N min 、 Particle diameter and adhesion distance Brownian motion step size (step), deposition rate (drop), and plotting step size; where the minimum cluster number N is... min The minimum number of clusters that determine complete reaction in the model is represented by the drawing step size, which represents the number of random Brownian motions during one drawing operation.

5. The method according to claim 2, characterized in that: In step 1, the three-dimensional spatial coordinates of each particle and its cluster information are stored in a structure, where X, Y, and Z represent the spatial coordinate components of each particle, and the cluster number Num records the cluster to which the particle belongs; the particle undergoes downward deposition motion while performing random Brownian motion.

6. The method according to claim 1, characterized in that: In step 3, the method steps for model validation are as follows: ① By changing the silver ion concentration and reduction reaction time, two preparation parameters were modified through experimental preparation methods to obtain flexible silver nanofilm samples with different preparation parameters; ② Scanning electron microscopy (SEM) images of flexible silver nanofilm samples under different preparation parameters were obtained. ③ Using electron microscopy scan images of flexible silver nanofilm samples, fractal dimension calculation methods were used to obtain fractal dimension parameters that can characterize the surface morphology of flexible silver nanofilm samples under different preparation parameters. ④ Using the same preparation parameters as in ①, set the particle concentration and reaction time parameters in the surface morphology fractal growth model respectively, and obtain the model simulation results under different parameters; ⑤ The simulation results of the model are processed into two dimensions, and the fractal dimension calculation method is used to obtain the fractal dimension parameters that characterize the surface morphology of the thin film in the model simulation. ⑥ Compare and analyze the fractal parameters calculated in ③ and ⑤ under different parameters to verify the accuracy and applicability of the established fractal growth model of the surface morphology of flexible silver nanofilm.

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