Method for determining internal micro-interface thermal resistance of a heat conducting gel system

Abstract

A method for determining the microscopic interfacial thermal resistance within a thermally conductive gel system belongs to the field of polymer materials technology. This invention includes: (1) designing a standard sample volume fraction, preparing a standard sample, and simultaneously measuring the particle size distribution and thermal conductivity; (2) establishing a structural model of the sample, using particle thermal conductivity, particle-matrix interfacial thermal resistance, and particle-particle interfacial thermal resistance as input parameters, performing high-throughput calculations of the macroscopic thermal conductivity, performing machine learning on the data, and obtaining a quantitative relationship prediction model and model coefficients; (3) obtaining the input parameter combination, substituting it into the quantitative relationship prediction model, predicting the thermal conductivity, and selecting the input parameter corresponding to the thermal conductivity closest to the experimental test results, thus determining the interfacial thermal resistance. This invention achieves reverse derivation of microscopic parameters through macroscopic calculation and testing, with low cost, simple operation, and accurate numerical results.

Description

Technical Field

[0001] This invention belongs to the field of polymer materials technology, specifically relating to a method for determining the thermal resistance of the internal micro-interface of a thermally conductive gel system. Background Technology

[0002] The miniaturization and increasing power of electronic packaging structures have led to a corresponding increase in the heat generated by electronic products, severely impacting device performance and lifespan. An effective method to address device heat dissipation is to fill the space between the chip and the heat sink with a thermal interface material possessing high thermal conductivity and good compressibility to reduce contact thermal resistance. Adding spherical particles with high thermal conductivity to polymers is the most common choice for thermal interface materials (thermal conductive gels). The rational selection of fillers and the adjustment of the filler-polymer matrix ratio are of great significance in both academic and industrial applications.

[0003] In thermally conductive gel systems, the interfacial thermal resistance between the filler and the matrix, as well as the interfacial thermal resistance among the fillers themselves, significantly impacts the system's macroscopic thermal conductivity. On one hand, one of the most effective methods for designing thermally conductive gel formulations is to use numerical models to predict and screen their thermal conductivity characteristics. This places high demands on the accuracy of the numerical models, requiring precise measurement of the interfacial thermal resistance. On the other hand, controlling the interfacial thermal resistance within the thermally conductive gel system through methods such as interface modification can effectively improve its thermal conductivity. This also necessitates quantitative measurement and characterization of the interfacial thermal resistance.

[0004] Determining interfacial thermal resistance at the microscale is extremely difficult. Currently, experimental methods mainly use the 3ω method and TDTR (time-domain thermal reflectance measurement system), while simulation methods are mainly based on molecular dynamics studies.

[0005] The aforementioned 3ω method and TDTR experimental methods require the deposition of metal electrodes or metal thin films on the polymer material surface, which affects the structure, electrical conductivity, and thermal conductivity of the film itself, thus the measurement results remain questionable. Currently, with the development of TDTR technology, although there are academic reports using TDTR and other testing methods, they are only applicable to specific material systems, and their high experimental costs and difficulties make it difficult to promote this method at present. From a simulation perspective, calculating interfacial thermal resistance using molecular dynamics methods is costly, complex in principle, and has very low accuracy.

[0006] This invention takes a novel approach, combining high-throughput computing, machine learning, and simple experimental testing to inversely deduce the microscopic interfacial thermal resistance characteristics of materials from their macroscopic thermal conductivity. It is low-cost, simple and easy to operate, and can achieve good testing accuracy. Summary of the Invention

[0007] To address the shortcomings of the existing technology, the present invention aims to provide a method for determining the microscopic interfacial thermal resistance within a thermally conductive gel system. This invention combines high-throughput computation, machine learning methods, and simple experimental testing to confirm the particle-matrix and particle-particle interfacial thermal resistances within the thermally conductive gel system.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] This invention relates to a scheme for determining the internal microscopic interfacial thermal resistance (including particle-matrix and particle-particle interfacial thermal resistance) in a spherical particle-filled polymer thermal interface material. First, a standard sample is designed and prepared, and its thermal conductivity is tested using a Rayleigh thermal conductivity meter. Then, a corresponding structural model is established based on the particle packing density in the standard sample, where the particles are completely randomly dispersed, and the particle size distribution is consistent with that in the sample. Further, based on the established structural model, using particle thermal conductivity and particle-matrix interfacial thermal resistance, and particle-particle interfacial thermal resistance as input parameters, random combinations of the input parameters are performed within a reasonable parameter range to conduct high-throughput calculations of the macroscopic thermal conductivity. Next, the large amount of data obtained from the high-throughput calculations is trained using machine learning methods to obtain a quantitative relationship model between the input parameters (particle and matrix thermal conductivity and particle-matrix interfacial thermal resistance, particle-particle interfacial thermal resistance) and the output parameter (thermal conductivity). Finally, based on this model, the data was filtered in reverse to obtain the input parameters corresponding to the numerical calculation results that matched the experimental test results, thus determining the microscopic interface thermal resistance inside the system.

[0010] A method for determining the internal micro-interfacial thermal resistance of a thermally conductive gel system, characterized by comprising the following steps:

[0011] (1) Design a standard sample volume fraction with particle filling degree. Based on the design, a standard sample is prepared using a high-speed mixer. At the same time, the particle size distribution and the thermal conductivity of the standard sample are measured.

[0012] (2) Based on the standard sample volume fraction designed in step (1) above, establish the sample structure model. Based on the established structure model, take particle thermal conductivity, particle-matrix interface thermal resistance and particle-particle interface thermal resistance as input parameters, randomly arrange and combine parameters within the parameter range, perform high-throughput calculation of macroscopic thermal conductivity, perform machine learning on the data obtained from the high-throughput calculation, obtain a quantitative relationship prediction model between input parameters and output parameters, i.e. thermal conductivity, and obtain the model coefficients.

[0013] (3) Select small interval values ​​within the range of input parameters and arrange them in combination to obtain the combination of input parameters. Substitute them into the quantitative relationship prediction model obtained in step (2) above to predict the output parameter, i.e., thermal conductivity. Select the input parameter corresponding to the thermal conductivity that is closest to the experimental test result, and thus determine the interface thermal resistance.

[0014] The method for determining the internal micro-interface thermal resistance of a thermally conductive gel system is characterized in that, in step (1), a silicone oil is used as the matrix and a silane coupling agent is added to ensure complete particle dispersion during the preparation of the sample using a high-speed stirrer.

[0015] The method for determining the internal microscopic interface thermal resistance of a thermally conductive gel system is characterized in that the particles in step (1) include single particles.

[0016] The method for determining the internal micro-interface thermal resistance of a thermally conductive gel system is characterized in that the particles in step (2) are completely randomly dispersed.

[0017] The method for determining the internal micro-interface thermal resistance of a thermally conductive gel system is characterized in that the particle size distribution in step (2) is consistent with the particle size distribution measured in step (1).

[0018] The method for determining the internal micro-interface thermal resistance of a thermally conductive gel system is characterized in that the method for determining the particle size distribution in step (1) includes a Malvern tester.

[0019] The method for determining the internal micro-interface thermal resistance of a thermally conductive gel system is characterized in that the method for measuring the thermal conductivity in step (1) includes a Ruiling thermal conductivity meter.

[0020] The method for determining the internal microscopic interface thermal resistance of a thermally conductive gel system is characterized in that the specific machine learning operation in step (2) is as follows: select three features from the simulation and experimental data, namely x1 x2, x1 x3, ..., x1 x2 x3, and generate 12 prototype functions for each feature. Among the 12 prototype functions for each feature, select the top three prototype functions by comparing the magnitude of the determination coefficient generated by least squares regression. Perform multiplication operations on the above three features to obtain 26 sets of prototype function expressions. Select the top three best-performing prototype functions in each set by least squares regression. Put the five features and the three prototype functions from the previous step together, and select the top 15 best-performing prototype functions again. Use the curve fit method to generate a quantitative relationship prediction model using the above 15 prototype functions and obtain the model coefficients.

[0021] The method for determining the internal microscopic interface thermal resistance of a thermally conductive gel system is characterized in that the 26 sets of prototype function expressions are derived based on the fact that each of the three features has three prototype functions.

[0022] The method for determining the microscopic interfacial thermal resistance within a thermally conductive gel system described above is applied to the accurate prediction of interfacial thermal resistance in thermally conductive gel systems.

[0023] The present invention has the following beneficial effects:

[0024] 1. This invention is the first to propose a method that combines high-throughput computing, machine learning and simple experimental preparation and testing to determine the interfacial thermal resistance in thermally conductive gel systems, and realizes the reverse derivation of microscopic parameters through macroscopic calculation and testing.

[0025] 2. This method is low-cost, simple to operate, and yields accurate values ​​for determining the microscopic interfacial thermal resistance within a system. Attached Figure Description

[0026] Figure 1 A schematic diagram of the structural model of the standard specimen;

[0027] Figure 2 A flowchart of machine learning methods;

[0028] Figure 3 This is a flowchart of the technical solution of the present invention. Detailed Implementation

[0029] The present invention will be further described in conjunction with the accompanying drawings and embodiments.

[0030] Example 1:

[0031] This invention selects the macroscopic thermal conductivity of the thermal interface material with high thermal conductivity particles as the research object, and adopts the following technical solution to determine the internal microscopic interface thermal resistance:

[0032] 1) Design, preparation and experimental testing of standard samples

[0033] Standard samples with a certain particle filling degree were designed. Taking single-particle filling as an example, three samples with different volume fractions were designed: 55 vol%, 60 vol%, and 65 vol%. These samples were prepared using a high-speed mixer according to the design. The matrix was silicone oil, with an appropriate amount of silane coupling agent added to ensure complete particle dispersion. Simultaneously, the particle size distribution was determined using a Malvern spectrometer, and the thermal conductivity of the prepared samples was measured using a Rayleigh thermal conductivity meter.

[0034] 2) Establishment of sample structure model, high-throughput computing and machine learning

[0035] A structural model of the sample was established based on the filling ratio of the designed standard sample, wherein the particles were completely randomly dispersed, and the particle size distribution met the results obtained from the Malvern tester. Figure 1 As shown. For each structural model, its macroscopic thermal conductivity is calculated using high-throughput calculations with particle thermal conductivity, particle-matrix interface thermal resistance, and particle-particle interface thermal resistance as input parameters within a reasonable range. Taking alumina particles as an example, the thermal conductivity of alumina particles is selected as [20, 25, 30, 35, 40] W / mK, and the thermal conductivity of both particle-matrix and particle-particle interfaces is

[10] . -9 5*10 -9 10 -8 5*10 -8 10 -7 5*10 -7 10 -6 5*10 -6 10 -5 5*10 -5 ]m 2 The input parameters K / W are randomly combined to form 500 sets of input data. We can then calculate the system thermal conductivity corresponding to these 500 sets of input parameters, form a database, and perform machine learning on this data.

[0036] like Figure 2 As shown, our machine learning strategy for constructing the predictive model is illustrated. We first select three features (x1 x2, x1 x3, ..., x1 x2 x3) from the simulated and experimental data, and generate 12 prototype functions for each feature. Among the 12 prototype functions for each feature, we select the top three best-performing prototype functions by comparing the magnitude of the coefficient of determination (R²) generated by least squares regression (LSR).

[0037] After least squares regression, each feature retains 3 prototype functions. Then, we perform multiplication operations on the permutations and combinations of the 3 features (x1 x2, x1x3, ..., x1 x2 x3) (e.g., the expression for x1 x2 is x1*x2), resulting in a total of 26 expressions. Because each feature has 3 prototype functions, each combination contains multiple prototype function expressions. We again use the LSR method to select the top 3 best-performing prototype functions from each combination. Then, we combine the 5 features with the best-performing prototype functions from the previous step and select the top 15 best-performing prototype functions again. Finally, using the curve fit method (SciPy documentation, nd), we use the 15 best-performing prototype functions to generate the predictive model and obtain the model coefficients.

[0038] 3) Reverse determination of interfacial thermal resistance

[0039] By selecting values ​​at very small intervals within a reasonable range of input parameters and arranging and combining them, a large number of input parameter combinations are obtained. These combinations are then fed into the model obtained by the aforementioned machine learning method to predict the output parameter (i.e., thermal conductivity). The input parameter corresponding to the output parameter that most closely matches the experimental test results is selected, thus determining the interfacial thermal resistance. Figure 3 This is a flowchart of the technical solution of the present invention. The present invention has been tested and proven to be feasible.

Claims

1. A method for determining the internal microscopic interfacial thermal resistance of a thermally conductive gel system, characterized by The method comprises the following steps: (1) designing a series of standard samples with different particle filling volume fractions, preparing the standard samples by using a high-speed mixer according to the design, and measuring the particle size distribution and the thermal conductivity of the standard samples; (2) establishing a physical structure model of the standard sample according to the particle volume fraction in the standard sample designed in step (1), taking the particle thermal conductivity, the particle-matrix interface thermal resistance and the particle-particle interface thermal resistance as input parameters, randomly arranging and combining the parameters in the parameter range, performing high-throughput calculation of the thermal conductivity, performing machine learning on the data obtained by the high-throughput calculation, obtaining a quantitative relationship prediction model between the input parameters, i.e., the particle-matrix interface thermal resistance and the particle-particle interface thermal resistance, and the output parameter, i.e., the thermal conductivity, and obtaining model coefficients; (3) selecting small interval values in the input parameter range, arranging and combining the values, obtaining input parameter combinations, and substituting the input parameter combinations into the quantitative relationship prediction model obtained in step (2) to predict the output parameter, i.e., the thermal conductivity, and selecting the input parameter corresponding to the thermal conductivity closest to the thermal conductivity of the standard sample measured in step (1), i.e., determining the micro-interface thermal resistance of the standard sample. The micro-interface thermal resistance includes the particle-matrix interface thermal resistance and the particle-particle interface thermal resistance.

2. The method of determining the internal micro-interface thermal resistance of a thermally conductive gel system of claim 1, wherein In the process of preparing the sample by using the high-speed mixer in step (1), silicone oil is used as the matrix, and silane coupling agent is added to ensure complete dispersion of the particles.

3. The method of determining the internal micro-interface thermal resistance of a thermally conductive gel system of claim 1, wherein The particles in step (1) include single particles.

4. The method of determining the internal microscopical interfacial thermal resistance of a heat conducting gel system according to claim 1, characterized in that The particles in step (2) are completely randomly dispersed.

5. The method of determining the internal micro-interface thermal resistance of a thermally conductive gel system of claim 1, wherein The particle size distribution of the particles in step (2) is consistent with the particle size distribution measured in step (1).

6. The method of determining the internal microscopical interfacial thermal resistance of a heat conducting gel system according to claim 1, characterized in that The method for measuring the particle size distribution in step (1) includes a Malvern tester.

7. The method of determining the internal microscopical interfacial thermal resistance of a heat conducting gel system according to claim 1, characterized in that The method for measuring the thermal conductivity in step (1) includes a Swihart thermal conductivity tester.

8. The method of determining the internal microscopical interfacial thermal resistance of a heat conducting gel system according to claim 1, characterized in that The specific operation of machine learning in step (2) is as follows: three features are selected, x1, x2 and x3 are the particle thermal conductivity, the particle-matrix interface thermal resistance and the particle-particle interface thermal resistance, respectively, any combination is performed, 12 prototype functions are generated for each feature, in the 12 prototype functions of each feature, the first three prototype functions are selected by comparing the size of the determination coefficient generated by the least square regression, after the arrangement and combination of the three features, multiplication operation is performed, 26 groups of prototype function expressions are obtained, the first three prototype functions with the best performance are selected in each group by the method of least square regression, the three features and the three prototype functions in the last step are put together, the first 15 prototype functions with the best performance are selected again, a quantitative relationship prediction model is generated by the curve fit method using the above 15 prototype functions, and model coefficients are obtained.

9. A method of determining the internal microscopical interfacial thermal resistance of a thermally conductive gel system according to claim 8, characterized in that The 26 groups of prototype function expressions are obtained on the basis of three prototype functions for each of the three features.

10. Application of the method for determining the micro-interface thermal resistance in the thermal conductive gel system according to any one of claims 1-9 to accurately predict the interface thermal resistance in the thermal conductive gel system.

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